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<div class="header">
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<div class="title">BDCSVD.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// We used the &quot;A Divide-And-Conquer Algorithm for the Bidiagonal SVD&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// research report written by Ming Gu and Stanley C.Eisenstat</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// The code variable names correspond to the names they used in their</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// report</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Copyright (C) 2013 Gauthier Brun &lt;brun.gauthier@gmail.com&gt;</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// Copyright (C) 2013 Nicolas Carre &lt;nicolas.carre@ensimag.fr&gt;</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">// Copyright (C) 2013 Jean Ceccato &lt;jean.ceccato@ensimag.fr&gt;</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// Copyright (C) 2013 Pierre Zoppitelli &lt;pierre.zoppitelli@ensimag.fr&gt;</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// Copyright (C) 2013 Jitse Niesen &lt;jitse@maths.leeds.ac.uk&gt;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// Copyright (C) 2014-2017 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#ifndef EIGEN_BDCSVD_H</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="preprocessor">#define EIGEN_BDCSVD_H</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment">// #define EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment">// #define EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160; </div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#undef eigen_internal_assert</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="preprocessor">#define eigen_internal_assert(X) assert(X);</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160; </div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;IOFormat bdcsvdfmt(8, 0, <span class="stringliteral">&quot;, &quot;</span>, <span class="stringliteral">&quot;\n&quot;</span>, <span class="stringliteral">&quot;  [&quot;</span>, <span class="stringliteral">&quot;]&quot;</span>);</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="keyword">class </span>BDCSVD;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160; </div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160; </div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="keyword">struct </span>traits&lt;BDCSVD&lt;MatrixType_, Options&gt; &gt; : svd_traits&lt;MatrixType_, Options&gt; {</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;};</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="keyword">struct </span>allocate_small_svd {</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(JacobiSVD&lt;MatrixType, Options&gt;&amp; smallSvd, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    (void)computationOptions;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    smallSvd = JacobiSVD&lt;MatrixType, Options&gt;(rows, cols);</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  }</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;};</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;<span class="keyword">struct </span>allocate_small_svd&lt;MatrixType, 0&gt; {</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(JacobiSVD&lt;MatrixType&gt;&amp; smallSvd, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    smallSvd = JacobiSVD&lt;MatrixType&gt;(rows, cols, computationOptions);</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  }</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;};</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> Options_&gt;</div>
<div class="line"><a name="l00097"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html">   97</a></span>&#160;<span class="keyword">class </span><a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD</a> : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SVDBase.html">SVDBase</a>&lt;BDCSVD&lt;MatrixType_, Options_&gt; &gt; {</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SVDBase.html">SVDBase&lt;BDCSVD&gt;</a> <a class="code" href="structEigen_1_1EigenBase.html">Base</a>;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="keyword">using</span> Base::rows;</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  <span class="keyword">using</span> Base::cols;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  <span class="keyword">using</span> <a class="code" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">Base::computeU</a>;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  <span class="keyword">using</span> <a class="code" href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">Base::computeV</a>;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::Scalar Scalar;</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::RealScalar RealScalar;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;RealScalar&gt;::Literal</a> Literal;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1SVDBase.html#a6229a37997eca1072b52cca5ee7a2bec">Base::Index</a> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    Options = Options_,</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    RowsAtCompileTime = Base::RowsAtCompileTime,</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    ColsAtCompileTime = Base::ColsAtCompileTime,</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    DiagSizeAtCompileTime = Base::DiagSizeAtCompileTime,</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    MaxRowsAtCompileTime = Base::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    MaxColsAtCompileTime = Base::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    MaxDiagSizeAtCompileTime = Base::MaxDiagSizeAtCompileTime,</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    MatrixOptions = Base::MatrixOptions</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  };</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160; </div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::MatrixUType MatrixUType;</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::MatrixVType MatrixVType;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::SingularValuesType SingularValuesType;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160; </div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar, Dynamic, Dynamic, ColMajor&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">MatrixX</a>;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;RealScalar, Dynamic, Dynamic, ColMajor&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">MatrixXr</a>;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;RealScalar, Dynamic, 1&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">VectorType</a>;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Array.html">Array&lt;RealScalar, Dynamic, 1&gt;</a> <a class="code" href="classEigen_1_1Array.html">ArrayXr</a>;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Array.html">Array&lt;Index,1,Dynamic&gt;</a> <a class="code" href="classEigen_1_1Array.html">ArrayXi</a>;</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Ref.html">Ref&lt;ArrayXr&gt;</a> <a class="code" href="classEigen_1_1Ref.html">ArrayRef</a>;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Ref.html">Ref&lt;ArrayXi&gt;</a> <a class="code" href="classEigen_1_1Ref.html">IndicesRef</a>;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
<div class="line"><a name="l00139"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a9c247985636005f4aef20bc92f713cd3">  139</a></span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html#a9c247985636005f4aef20bc92f713cd3">BDCSVD</a>() : m_algoswap(16), m_isTranspose(false), m_compU(false), m_compV(false), m_numIters(0)</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  {}</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160; </div>
<div class="line"><a name="l00148"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#afa37310e3f27088f3e825f59ab822ef9">  148</a></span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html#afa37310e3f27088f3e825f59ab822ef9">BDCSVD</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1BDCSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1BDCSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    allocate(<a class="code" href="classEigen_1_1BDCSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="classEigen_1_1BDCSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, internal::get_computation_options(Options));</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  }</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;  EIGEN_DEPRECATED</div>
<div class="line"><a name="l00167"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a7d9fac78e0c239b2e8e92cd189932f21">  167</a></span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html#a7d9fac78e0c239b2e8e92cd189932f21">BDCSVD</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1BDCSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="classEigen_1_1BDCSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    internal::check_svd_options_assertions&lt;MatrixType, Options&gt;(computationOptions, <a class="code" href="classEigen_1_1BDCSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="classEigen_1_1BDCSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    allocate(<a class="code" href="classEigen_1_1BDCSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, <a class="code" href="classEigen_1_1BDCSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, computationOptions);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160; </div>
<div class="line"><a name="l00177"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a586d8a4d76bb40f315f8ae290419abf3">  177</a></span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html#a586d8a4d76bb40f315f8ae290419abf3">BDCSVD</a>(<span class="keyword">const</span> MatrixType&amp; matrix) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    compute_impl(matrix, internal::get_computation_options(Options));</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;  }</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160; </div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  EIGEN_DEPRECATED</div>
<div class="line"><a name="l00194"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a30778887eb456715a333ccf9cb75f14e">  194</a></span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html#a30778887eb456715a333ccf9cb75f14e">BDCSVD</a>(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) : m_algoswap(16), m_numIters(0) {</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;    internal::check_svd_options_assertions&lt;MatrixType, Options&gt;(computationOptions, matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    compute_impl(matrix, computationOptions);</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  }</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  ~<a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD</a>() {}</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#a1d4028e15977308117e7ead7a21feee9">  206</a></span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD</a>&amp; <a class="code" href="classEigen_1_1BDCSVD.html#a1d4028e15977308117e7ead7a21feee9">compute</a>(<span class="keyword">const</span> MatrixType&amp; matrix) { <span class="keywordflow">return</span> compute_impl(matrix, m_computationOptions); }</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;  EIGEN_DEPRECATED</div>
<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="classEigen_1_1BDCSVD.html#ada8a7edd2ddc8ab10fdea4b1b7c1b838">  218</a></span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD</a>&amp; <a class="code" href="classEigen_1_1BDCSVD.html#ada8a7edd2ddc8ab10fdea4b1b7c1b838">compute</a>(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;    internal::check_svd_options_assertions&lt;MatrixType, Options&gt;(computationOptions, matrix.rows(), matrix.cols());</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    <span class="keywordflow">return</span> compute_impl(matrix, computationOptions);</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  }</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160; </div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  <span class="keywordtype">void</span> setSwitchSize(<span class="keywordtype">int</span> s)</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  {</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    eigen_assert(s&gt;=3 &amp;&amp; <span class="stringliteral">&quot;BDCSVD the size of the algo switch has to be at least 3.&quot;</span>);</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    m_algoswap = s;</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  }</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;  <span class="keywordtype">void</span> allocate(Index <a class="code" href="classEigen_1_1BDCSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>, Index <a class="code" href="classEigen_1_1BDCSVD.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;  <a class="code" href="classEigen_1_1BDCSVD.html#a9c247985636005f4aef20bc92f713cd3">BDCSVD</a>&amp; compute_impl(<span class="keyword">const</span> MatrixType&amp; matrix, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions);</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;  <span class="keywordtype">void</span> divide(Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift);</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  <span class="keywordtype">void</span> computeSVDofM(Index firstCol, Index n, MatrixXr&amp; U, VectorType&amp; singVals, MatrixXr&amp; V);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  <span class="keywordtype">void</span> computeSingVals(<span class="keyword">const</span> ArrayRef&amp; col0, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef&amp; perm, VectorType&amp; singVals, ArrayRef shifts, ArrayRef mus);</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  <span class="keywordtype">void</span> perturbCol0(<span class="keyword">const</span> ArrayRef&amp; col0, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef&amp; perm, <span class="keyword">const</span> VectorType&amp; singVals, <span class="keyword">const</span> ArrayRef&amp; shifts, <span class="keyword">const</span> ArrayRef&amp; mus, ArrayRef zhat);</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  <span class="keywordtype">void</span> computeSingVecs(<span class="keyword">const</span> ArrayRef&amp; zhat, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef&amp; perm, <span class="keyword">const</span> VectorType&amp; singVals, <span class="keyword">const</span> ArrayRef&amp; shifts, <span class="keyword">const</span> ArrayRef&amp; mus, MatrixXr&amp; U, MatrixXr&amp; V);</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  <span class="keywordtype">void</span> deflation43(Index firstCol, Index shift, Index i, Index <a class="code" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>);</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  <span class="keywordtype">void</span> deflation44(Index firstColu , Index firstColm, Index firstRowW, Index firstColW, Index i, Index j, Index <a class="code" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>);</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keywordtype">void</span> deflation(Index firstCol, Index lastCol, Index k, Index firstRowW, Index firstColW, Index shift);</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> HouseholderU, <span class="keyword">typename</span> HouseholderV, <span class="keyword">typename</span> NaiveU, <span class="keyword">typename</span> NaiveV&gt;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  <span class="keywordtype">void</span> copyUV(<span class="keyword">const</span> HouseholderU &amp;householderU, <span class="keyword">const</span> HouseholderV &amp;householderV, <span class="keyword">const</span> NaiveU &amp;naiveU, <span class="keyword">const</span> NaiveV &amp;naivev);</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  <span class="keywordtype">void</span> structured_update(Block&lt;MatrixXr,Dynamic,Dynamic&gt; A, <span class="keyword">const</span> MatrixXr &amp;B, Index n1);</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="keyword">static</span> RealScalar secularEq(RealScalar x, <span class="keyword">const</span> ArrayRef&amp; col0, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef &amp;perm, <span class="keyword">const</span> ArrayRef&amp; diagShifted, RealScalar shift);</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="keyword">template</span> &lt;<span class="keyword">typename</span> SVDType&gt;</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  <span class="keywordtype">void</span> computeBaseCase(SVDType&amp; svd, Index n, Index firstCol, Index firstRowW, Index firstColW, Index shift);</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160; </div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160; <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  MatrixXr m_naiveU, m_naiveV;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  MatrixXr m_computed;</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  Index m_nRec;</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  ArrayXr m_workspace;</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  ArrayXi m_workspaceI;</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  <span class="keywordtype">int</span> m_algoswap;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  <span class="keywordtype">bool</span> m_isTranspose, m_compU, m_compV;</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  JacobiSVD&lt;MatrixType, Options&gt; smallSvd;</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160; </div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  <span class="keyword">using</span> Base::m_computationOptions;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  <span class="keyword">using</span> Base::m_computeThinU;</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  <span class="keyword">using</span> Base::m_computeThinV;</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;  <span class="keyword">using</span> Base::m_diagSize;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  <span class="keyword">using</span> Base::m_info;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;  <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  <span class="keyword">using</span> Base::m_matrixU;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  <span class="keyword">using</span> Base::m_matrixV;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  <span class="keyword">using</span> Base::m_nonzeroSingularValues;</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  <span class="keyword">using</span> Base::m_singularValues;</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160; </div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <span class="keywordtype">int</span> m_numIters;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;};  <span class="comment">// end class BDCSVD</span></div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160; </div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;<span class="comment">// Method to allocate and initialize matrix and attributes</span></div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::allocate(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;  <span class="keywordflow">if</span> (Base::allocate(rows, cols, computationOptions))</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160; </div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  <span class="keywordflow">if</span> (cols &lt; m_algoswap)</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    internal::allocate_small_svd&lt;MatrixType, Options&gt;::run(smallSvd, rows, cols, computationOptions);</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160; </div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  m_computed = MatrixXr::Zero(m_diagSize + 1, m_diagSize );</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  m_compU = computeV();</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;  m_compV = computeU();</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  m_isTranspose = (cols &gt; rows);</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  <span class="keywordflow">if</span> (m_isTranspose)</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    std::swap(m_compU, m_compV);</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160; </div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;  <span class="keywordflow">if</span> (m_compU) m_naiveU = MatrixXr::Zero(m_diagSize + 1, m_diagSize + 1 );</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;  <span class="keywordflow">else</span>         m_naiveU = MatrixXr::Zero(2, m_diagSize + 1 );</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160; </div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  <span class="keywordflow">if</span> (m_compV) m_naiveV = MatrixXr::Zero(m_diagSize, m_diagSize);</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160; </div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  m_workspace.resize((m_diagSize+1)*(m_diagSize+1)*3);</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;  m_workspaceI.resize(3*m_diagSize);</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;}  <span class="comment">// end allocate</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160; </div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;BDCSVD&lt;MatrixType, Options&gt;&amp; BDCSVD&lt;MatrixType, Options&gt;::compute_impl(<span class="keyword">const</span> MatrixType&amp; matrix,</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;                                                                       <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions) {</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;\n\n\n======================================================================================================================\n\n\n&quot;</span>;</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160; </div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  allocate(matrix.rows(), matrix.cols(), computationOptions);</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160; </div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;  <span class="keyword">const</span> RealScalar considerZero = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160; </div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  <span class="comment">//**** step -1 - If the problem is too small, directly falls back to JacobiSVD and return</span></div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  <span class="keywordflow">if</span>(matrix.cols() &lt; m_algoswap)</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  {</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    smallSvd.compute(matrix);</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;    m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    m_info = smallSvd.info();</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    <span class="keywordflow">if</span> (m_info == <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a> || m_info == <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>) {</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;      <span class="keywordflow">if</span> (computeU()) m_matrixU = smallSvd.matrixU();</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;      <span class="keywordflow">if</span> (computeV()) m_matrixV = smallSvd.matrixV();</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;      m_singularValues = smallSvd.singularValues();</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;      m_nonzeroSingularValues = smallSvd.nonzeroSingularValues();</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    }</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  }</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160; </div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  <span class="comment">//**** step 0 - Copy the input matrix and apply scaling to reduce over/under-flows</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;  RealScalar scale = matrix.cwiseAbs().template maxCoeff&lt;PropagateNaN&gt;();</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;  <span class="keywordflow">if</span> (!(numext::isfinite)(scale)) {</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;    m_info = <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf">InvalidInput</a>;</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  }</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160; </div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  <span class="keywordflow">if</span>(numext::is_exactly_zero(scale)) scale = Literal(1);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  <a class="code" href="group__matrixtypedefs.html#ga8a779d79defc9f822fa6ff5869c2ba6b">MatrixX</a> copy;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  <span class="keywordflow">if</span> (m_isTranspose) copy = matrix.adjoint()/scale;</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  <span class="keywordflow">else</span>               copy = matrix/scale;</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160; </div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  <span class="comment">//**** step 1 - Bidiagonalization</span></div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  <span class="comment">// FIXME this line involves temporaries</span></div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  internal::UpperBidiagonalization&lt;MatrixX&gt; bid(copy);</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160; </div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  <span class="comment">//**** step 2 - Divide &amp; Conquer</span></div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  m_naiveU.setZero();</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  m_naiveV.setZero();</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  <span class="comment">// FIXME this line involves a temporary matrix</span></div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  m_computed.topRows(m_diagSize) = bid.bidiagonal().toDenseMatrix().transpose();</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;  m_computed.template bottomRows&lt;1&gt;().setZero();</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  divide(0, m_diagSize - 1, 0, 0, 0);</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  <span class="keywordflow">if</span> (m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a> &amp;&amp; m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>) {</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  }</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160; </div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;  <span class="comment">//**** step 3 - Copy singular values and vectors</span></div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i&lt;m_diagSize; i++)</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  {</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    RealScalar a = <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_computed.coeff(i, i));</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    m_singularValues.coeffRef(i) = a * scale;</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    <span class="keywordflow">if</span> (a&lt;considerZero)</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    {</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;      m_nonzeroSingularValues = i;</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;      m_singularValues.tail(m_diagSize - i - 1).setZero();</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    }</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i == m_diagSize - 1)</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    {</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;      m_nonzeroSingularValues = i + 1;</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;      <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;    }</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  }</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160; </div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;<span class="comment">//   std::cout &lt;&lt; &quot;m_naiveU\n&quot; &lt;&lt; m_naiveU &lt;&lt; &quot;\n\n&quot;;</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;<span class="comment">//   std::cout &lt;&lt; &quot;m_naiveV\n&quot; &lt;&lt; m_naiveV &lt;&lt; &quot;\n\n&quot;;</span></div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;  <span class="keywordflow">if</span>(m_isTranspose) copyUV(bid.householderV(), bid.householderU(), m_naiveV, m_naiveU);</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;  <span class="keywordflow">else</span>              copyUV(bid.householderU(), bid.householderV(), m_naiveU, m_naiveV);</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160; </div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;}  <span class="comment">// end compute</span></div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160; </div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> HouseholderU, <span class="keyword">typename</span> HouseholderV, <span class="keyword">typename</span> NaiveU, <span class="keyword">typename</span> NaiveV&gt;</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::copyUV(<span class="keyword">const</span> HouseholderU&amp; householderU, <span class="keyword">const</span> HouseholderV&amp; householderV,</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;                                         <span class="keyword">const</span> NaiveU&amp; naiveU, <span class="keyword">const</span> NaiveV&amp; naiveV) {</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;  <span class="comment">// Note exchange of U and V: m_matrixU is set from m_naiveV and vice versa</span></div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;  <span class="keywordflow">if</span> (computeU())</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;  {</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> Ucols = m_computeThinU ? m_diagSize : householderU.cols();</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    m_matrixU = <a class="code" href="classEigen_1_1MatrixBase.html#a98bb9a0f705c6dfde85b0bfff31bf88f">MatrixX::Identity</a>(householderU.cols(), Ucols);</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    m_matrixU.topLeftCorner(m_diagSize, m_diagSize) = naiveV.template cast&lt;Scalar&gt;().topLeftCorner(m_diagSize, m_diagSize);</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    householderU.applyThisOnTheLeft(m_matrixU); <span class="comment">// FIXME this line involves a temporary buffer</span></div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;  }</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  <span class="keywordflow">if</span> (computeV())</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  {</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> Vcols = m_computeThinV ? m_diagSize : householderV.cols();</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    m_matrixV = <a class="code" href="classEigen_1_1MatrixBase.html#a98bb9a0f705c6dfde85b0bfff31bf88f">MatrixX::Identity</a>(householderV.cols(), Vcols);</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    m_matrixV.topLeftCorner(m_diagSize, m_diagSize) = naiveU.template cast&lt;Scalar&gt;().topLeftCorner(m_diagSize, m_diagSize);</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    householderV.applyThisOnTheLeft(m_matrixV); <span class="comment">// FIXME this line involves a temporary buffer</span></div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;  }</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;}</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160; </div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::structured_update(Block&lt;MatrixXr, Dynamic, Dynamic&gt; A, <span class="keyword">const</span> MatrixXr&amp; B, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n1) {</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = A.rows();</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;  <span class="keywordflow">if</span>(n&gt;100)</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;  {</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    <span class="comment">// If the matrices are large enough, let&#39;s exploit the sparse structure of A by</span></div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;    <span class="comment">// splitting it in half (wrt n1), and packing the non-zero columns.</span></div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n2 = n - n1;</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    Map&lt;MatrixXr&gt; A1(m_workspace.data()      , n1, n);</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;    Map&lt;MatrixXr&gt; A2(m_workspace.data()+ n1*n, n2, n);</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;    Map&lt;MatrixXr&gt; B1(m_workspace.data()+  n*n, n,  n);</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;    Map&lt;MatrixXr&gt; B2(m_workspace.data()+2*n*n, n,  n);</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k1=0, k2=0;</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j=0; j&lt;n; ++j)</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;    {</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;      <span class="keywordflow">if</span>( (A.col(j).head(n1).array()!=Literal(0)).any() )</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;      {</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;        A1.col(k1) = A.col(j).head(n1);</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;        B1.row(k1) = B.row(j);</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;        ++k1;</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;      }</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;      <span class="keywordflow">if</span>( (A.col(j).tail(n2).array()!=Literal(0)).any() )</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;      {</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;        A2.col(k2) = A.col(j).tail(n2);</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;        B2.row(k2) = B.row(j);</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;        ++k2;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;      }</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    }</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160; </div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    A.topRows(n1).noalias()    = A1.leftCols(k1) * B1.topRows(k1);</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    A.bottomRows(n2).noalias() = A2.leftCols(k2) * B2.topRows(k2);</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;  }</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  {</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    Map&lt;MatrixXr,Aligned&gt; tmp(m_workspace.data(),n,n);</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    tmp.noalias() = A*B;</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    A = tmp;</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  }</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;}</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160; </div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> SVDType&gt;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::computeBaseCase(SVDType&amp; svd, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstCol, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstRowW,</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;                                                  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstColW, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> shift) {</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;  svd.compute(m_computed.block(firstCol, firstCol, n + 1, n));</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;  m_info = svd.info();</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;  <span class="keywordflow">if</span> (m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a> &amp;&amp; m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;  <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;    m_naiveU.block(firstCol, firstCol, n + 1, n + 1).real() = svd.matrixU();</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;  <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;    m_naiveU.row(0).segment(firstCol, n + 1).real() = svd.matrixU().row(0);</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;    m_naiveU.row(1).segment(firstCol, n + 1).real() = svd.matrixU().row(n);</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  }</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;  <span class="keywordflow">if</span> (m_compV) m_naiveV.block(firstRowW, firstColW, n, n).real() = svd.matrixV();</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;  m_computed.block(firstCol + shift, firstCol + shift, n + 1, n).setZero();</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  m_computed.diagonal().segment(firstCol + shift, n) = svd.singularValues().head(n);</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;}</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160; </div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;<span class="comment">// The divide algorithm is done &quot;in place&quot;, we are always working on subsets of the same matrix. The divide methods</span></div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;<span class="comment">// takes as argument the place of the submatrix we are currently working on.</span></div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160; </div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;<span class="comment">//@param firstCol : The Index of the first column of the submatrix of m_computed and for m_naiveU;</span></div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;<span class="comment">//@param lastCol : The Index of the last column of the submatrix of m_computed and for m_naiveU;</span></div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;<span class="comment">// lastCol + 1 - firstCol is the size of the submatrix.</span></div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;<span class="comment">//@param firstRowW : The Index of the first row of the matrix W that we are to change. (see the reference paper section 1 for more information on W)</span></div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;<span class="comment">//@param firstColW : Same as firstRowW with the column.</span></div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;<span class="comment">//@param shift : Each time one takes the left submatrix, one must add 1 to the shift. Why? Because! We actually want the last column of the U submatrix</span></div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;<span class="comment">// to become the first column (*coeff) and to shift all the other columns to the right. There are more details on the reference paper.</span></div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::divide(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstCol, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> lastCol, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstRowW,</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;                                         <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstColW, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> shift) {</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;  <span class="comment">// requires rows = cols + 1;</span></div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = lastCol - firstCol + 1;</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = n/2;</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;  <span class="keyword">const</span> RealScalar considerZero = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  RealScalar alphaK;</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;  RealScalar betaK;</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;  RealScalar r0;</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  RealScalar lambda, phi, c0, s0;</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;  VectorType l, f;</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;  <span class="comment">// We use the other algorithm which is more efficient for small</span></div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;  <span class="comment">// matrices.</span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;  <span class="keywordflow">if</span> (n &lt; m_algoswap)</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;  {</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;    <span class="comment">// FIXME this block involves temporaries</span></div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;    <span class="keywordflow">if</span> (m_compV) {</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;      JacobiSVD&lt;MatrixXr, ComputeFullU | ComputeFullV&gt; baseSvd;</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;      computeBaseCase(baseSvd, n, firstCol, firstRowW, firstColW, shift);</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;    } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;      JacobiSVD&lt;MatrixXr, ComputeFullU&gt; baseSvd;</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;      computeBaseCase(baseSvd, n, firstCol, firstRowW, firstColW, shift);</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;    }</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  }</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  <span class="comment">// We use the divide and conquer algorithm</span></div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;  alphaK =  m_computed(firstCol + k, firstCol + k);</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;  betaK = m_computed(firstCol + k + 1, firstCol + k);</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;  <span class="comment">// The divide must be done in that order in order to have good results. Divide change the data inside the submatrices</span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  <span class="comment">// and the divide of the right submatrice reads one column of the left submatrice. That&#39;s why we need to treat the</span></div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  <span class="comment">// right submatrix before the left one.</span></div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  divide(k + 1 + firstCol, lastCol, k + 1 + firstRowW, k + 1 + firstColW, shift);</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;  <span class="keywordflow">if</span> (m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a> &amp;&amp; m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;  divide(firstCol, k - 1 + firstCol, firstRowW, firstColW + 1, shift + 1);</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;  <span class="keywordflow">if</span> (m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a> &amp;&amp; m_info != <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>) <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160; </div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  {</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;    lambda = m_naiveU(firstCol + k, firstCol + k);</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;    phi = m_naiveU(firstCol + k + 1, lastCol + 1);</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  }</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  {</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    lambda = m_naiveU(1, firstCol + k);</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;    phi = m_naiveU(0, lastCol + 1);</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;  }</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;  r0 = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>((<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(alphaK * lambda) * <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(alphaK * lambda)) + <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(betaK * phi) * <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(betaK * phi));</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;  <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;  {</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;    l = m_naiveU.row(firstCol + k).segment(firstCol, k);</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;    f = m_naiveU.row(firstCol + k + 1).segment(firstCol + k + 1, n - k - 1);</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;  }</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;  {</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;    l = m_naiveU.row(1).segment(firstCol, k);</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;    f = m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1);</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;  }</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;  <span class="keywordflow">if</span> (m_compV) m_naiveV(firstRowW+k, firstColW) = Literal(1);</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  <span class="keywordflow">if</span> (r0&lt;considerZero)</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;  {</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;    c0 = Literal(1);</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;    s0 = Literal(0);</div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  }</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;  {</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;    c0 = alphaK * lambda / r0;</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    s0 = betaK * phi / r0;</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;  }</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160; </div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;  assert(m_naiveU.allFinite());</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  assert(m_naiveV.allFinite());</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;  assert(m_computed.allFinite());</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160; </div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;  <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;  {</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;    MatrixXr q1 (m_naiveU.col(firstCol + k).segment(firstCol, k + 1));</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;    <span class="comment">// we shiftW Q1 to the right</span></div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = firstCol + k - 1; i &gt;= firstCol; i--)</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;      m_naiveU.col(i + 1).segment(firstCol, k + 1) = m_naiveU.col(i).segment(firstCol, k + 1);</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;    <span class="comment">// we shift q1 at the left with a factor c0</span></div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;    m_naiveU.col(firstCol).segment( firstCol, k + 1) = (q1 * c0);</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;    <span class="comment">// last column = q1 * - s0</span></div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;    m_naiveU.col(lastCol + 1).segment(firstCol, k + 1) = (q1 * ( - s0));</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;    <span class="comment">// first column = q2 * s0</span></div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;    m_naiveU.col(firstCol).segment(firstCol + k + 1, n - k) = m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) * s0;</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;    <span class="comment">// q2 *= c0</span></div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;    m_naiveU.col(lastCol + 1).segment(firstCol + k + 1, n - k) *= c0;</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;  }</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  {</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;    RealScalar q1 = m_naiveU(0, firstCol + k);</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;    <span class="comment">// we shift Q1 to the right</span></div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = firstCol + k - 1; i &gt;= firstCol; i--)</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;      m_naiveU(0, i + 1) = m_naiveU(0, i);</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;    <span class="comment">// we shift q1 at the left with a factor c0</span></div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;    m_naiveU(0, firstCol) = (q1 * c0);</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;    <span class="comment">// last column = q1 * - s0</span></div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;    m_naiveU(0, lastCol + 1) = (q1 * ( - s0));</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;    <span class="comment">// first column = q2 * s0</span></div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;    m_naiveU(1, firstCol) = m_naiveU(1, lastCol + 1) *s0;</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;    <span class="comment">// q2 *= c0</span></div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;    m_naiveU(1, lastCol + 1) *= c0;</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;    m_naiveU.row(1).segment(firstCol + 1, k).setZero();</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;    m_naiveU.row(0).segment(firstCol + k + 1, n - k - 1).setZero();</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  }</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160; </div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  assert(m_naiveU.allFinite());</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  assert(m_naiveV.allFinite());</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;  assert(m_computed.allFinite());</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160; </div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;  m_computed(firstCol + shift, firstCol + shift) = r0;</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;  m_computed.col(firstCol + shift).segment(firstCol + shift + 1, k) = alphaK * l.transpose().real();</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;  m_computed.col(firstCol + shift).segment(firstCol + shift + k + 1, n - k - 1) = betaK * f.transpose().real();</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160; </div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;  ArrayXr tmp1 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;  <span class="comment">// Second part: try to deflate singular values in combined matrix</span></div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;  deflation(firstCol, lastCol, k, firstRowW, firstColW, shift);</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;  ArrayXr tmp2 = (m_computed.block(firstCol+shift, firstCol+shift, n, n)).jacobiSvd().singularValues();</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;\n\nj1 = &quot;</span> &lt;&lt; tmp1.transpose().format(bdcsvdfmt) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;j2 = &quot;</span> &lt;&lt; tmp2.transpose().format(bdcsvdfmt) &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;err:      &quot;</span> &lt;&lt; ((tmp1-tmp2).<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>()&gt;1e-12*tmp2.abs()).transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">int</span> count = 0;</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;# &quot;</span> &lt;&lt; ++count &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;  assert((tmp1-tmp2).matrix().norm() &lt; 1e-14*tmp2.matrix().norm());</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;<span class="comment">//   assert(count&lt;681);</span></div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;<span class="comment">//   assert(((tmp1-tmp2).abs()&lt;1e-13*tmp2.abs()).all());</span></div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160; </div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  <span class="comment">// Third part: compute SVD of combined matrix</span></div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;  MatrixXr UofSVD, VofSVD;</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;  VectorType singVals;</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;  computeSVDofM(firstCol + shift, n, UofSVD, singVals, VofSVD);</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160; </div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;  assert(UofSVD.allFinite());</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;  assert(VofSVD.allFinite());</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160; </div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;  <span class="keywordflow">if</span> (m_compU)</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;    structured_update(m_naiveU.block(firstCol, firstCol, n + 1, n + 1), UofSVD, (n+2)/2);</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;  {</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;    Map&lt;Matrix&lt;RealScalar,2,Dynamic&gt;,<a class="code" href="group__enums.html#gga45fe06e29902b7a2773de05ba27b47a1ae12d0f8f869c40c76128260af2242bc8">Aligned</a>&gt; tmp(m_workspace.data(),2,n+1);</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;    tmp.noalias() = m_naiveU.middleCols(firstCol, n+1) * UofSVD;</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;    m_naiveU.middleCols(firstCol, n + 1) = tmp;</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;  }</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160; </div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;  <span class="keywordflow">if</span> (m_compV)  structured_update(m_naiveV.block(firstRowW, firstColW, n, n), VofSVD, (n+1)/2);</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160; </div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;  assert(m_naiveU.allFinite());</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;  assert(m_naiveV.allFinite());</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;  assert(m_computed.allFinite());</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160; </div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;  m_computed.block(firstCol + shift, firstCol + shift, n, n).setZero();</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;  m_computed.block(firstCol + shift, firstCol + shift, n, n).diagonal() = singVals;</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;}  <span class="comment">// end divide</span></div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160; </div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;<span class="comment">// Compute SVD of m_computed.block(firstCol, firstCol, n + 1, n); this block only has non-zeros in</span></div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;<span class="comment">// the first column and on the diagonal and has undergone deflation, so diagonal is in increasing</span></div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;<span class="comment">// order except for possibly the (0,0) entry. The computed SVD is stored U, singVals and V, except</span></div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;<span class="comment">// that if m_compV is false, then V is not computed. Singular values are sorted in decreasing order.</span></div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;<span class="comment">// TODO Opportunities for optimization: better root finding algo, better stopping criterion, better</span></div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;<span class="comment">// handling of round-off errors, be consistent in ordering</span></div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;<span class="comment">// For instance, to solve the secular equation using FMM, see http://www.stat.uchicago.edu/~lekheng/courses/302/classics/greengard-rokhlin.pdf</span></div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::computeSVDofM(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstCol, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n, MatrixXr&amp; U,</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;                                                VectorType&amp; singVals, MatrixXr&amp; V) {</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;  <span class="keyword">const</span> RealScalar considerZero = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;  ArrayRef col0 = m_computed.col(firstCol).segment(firstCol, n);</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;  m_workspace.head(n) =  m_computed.block(firstCol, firstCol, n, n).diagonal();</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;  ArrayRef diag = m_workspace.head(n);</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;  diag(0) = Literal(0);</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160; </div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;  <span class="comment">// Allocate space for singular values and vectors</span></div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;  singVals.resize(n);</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;  U.resize(n+1, n+1);</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;  <span class="keywordflow">if</span> (m_compV) V.resize(n, n);</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160; </div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;  <span class="keywordflow">if</span> (col0.hasNaN() || diag.hasNaN())</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;    std::cout &lt;&lt; <span class="stringliteral">&quot;\n\nHAS NAN\n\n&quot;</span>;</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160; </div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;  <span class="comment">// Many singular values might have been deflated, the zero ones have been moved to the end,</span></div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;  <span class="comment">// but others are interleaved and we must ignore them at this stage.</span></div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;  <span class="comment">// To this end, let&#39;s compute a permutation skipping them:</span></div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> actual_n = n;</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;  <span class="keywordflow">while</span>(actual_n&gt;1 &amp;&amp; numext::is_exactly_zero(diag(actual_n - 1))) {</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;    --actual_n;</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;    eigen_internal_assert(numext::is_exactly_zero(col0(actual_n)));</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;  }</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = 0; <span class="comment">// size of the deflated problem</span></div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k=0;k&lt;actual_n;++k)</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;    <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(col0(k))&gt;considerZero)</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;      m_workspaceI(m++) = k;</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;  Map&lt;ArrayXi&gt; perm(m_workspaceI.data(),m);</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160; </div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;  Map&lt;ArrayXr&gt; shifts(m_workspace.data()+1*n, n);</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;  Map&lt;ArrayXr&gt; mus(m_workspace.data()+2*n, n);</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;  Map&lt;ArrayXr&gt; zhat(m_workspace.data()+3*n, n);</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160; </div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;computeSVDofM using:\n&quot;</span>;</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  z: &quot;</span> &lt;&lt; col0.transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  d: &quot;</span> &lt;&lt; diag.transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160; </div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;  <span class="comment">// Compute singVals, shifts, and mus</span></div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  computeSingVals(col0, diag, perm, singVals, shifts, mus);</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160; </div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  j:        &quot;</span> &lt;&lt; (m_computed.block(firstCol, firstCol, n, n)).jacobiSvd().singularValues().transpose().reverse() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  sing-val: &quot;</span> &lt;&lt; singVals.transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  mu:       &quot;</span> &lt;&lt; mus.transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  shift:    &quot;</span> &lt;&lt; shifts.transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160; </div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  {</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;    std::cout &lt;&lt; <span class="stringliteral">&quot;\n\n    mus:    &quot;</span> &lt;&lt; mus.head(actual_n).transpose() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;    std::cout &lt;&lt; <span class="stringliteral">&quot;    check1 (expect0) : &quot;</span> &lt;&lt; ((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n).transpose() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;    assert((((singVals.array()-(shifts+mus)) / singVals.array()).head(actual_n) &gt;= 0).all());</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;    std::cout &lt;&lt; <span class="stringliteral">&quot;    check2 (&gt;0)      : &quot;</span> &lt;&lt; ((singVals.array()-diag) / singVals.array()).head(actual_n).transpose() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;    assert((((singVals.array()-diag) / singVals.array()).head(actual_n) &gt;= 0).all());</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;  }</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160; </div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;  assert(singVals.allFinite());</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;  assert(mus.allFinite());</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;  assert(shifts.allFinite());</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160; </div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;  <span class="comment">// Compute zhat</span></div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;  perturbCol0(col0, diag, perm, singVals, shifts, mus, zhat);</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  zhat: &quot;</span> &lt;&lt; zhat.transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160; </div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;  assert(zhat.allFinite());</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160; </div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160;  computeSingVecs(zhat, diag, perm, singVals, shifts, mus, U, V);</div>
<div class="line"><a name="l00736"></a><span class="lineno">  736</span>&#160; </div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;U^T U: &quot;</span> &lt;&lt; (U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;V^T V: &quot;</span> &lt;&lt; (V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160; </div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;  assert(m_naiveU.allFinite());</div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;  assert(m_naiveV.allFinite());</div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;  assert(m_computed.allFinite());</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;  assert(U.allFinite());</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;  assert(V.allFinite());</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160;<span class="comment">//   assert((U.transpose() * U - MatrixXr(MatrixXr::Identity(U.cols(),U.cols()))).norm() &lt; 100*NumTraits&lt;RealScalar&gt;::epsilon() * n);</span></div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;<span class="comment">//   assert((V.transpose() * V - MatrixXr(MatrixXr::Identity(V.cols(),V.cols()))).norm() &lt; 100*NumTraits&lt;RealScalar&gt;::epsilon() * n);</span></div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160; </div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160;  <span class="comment">// Because of deflation, the singular values might not be completely sorted.</span></div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;  <span class="comment">// Fortunately, reordering them is a O(n) problem</span></div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=0; i&lt;actual_n-1; ++i)</div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;  {</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;    <span class="keywordflow">if</span>(singVals(i)&gt;singVals(i+1))</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;    {</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160;      <span class="keyword">using</span> std::swap;</div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;      swap(singVals(i),singVals(i+1));</div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;      U.col(i).swap(U.col(i+1));</div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160;      <span class="keywordflow">if</span>(m_compV) V.col(i).swap(V.col(i+1));</div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160;    }</div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;  }</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160; </div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;  {</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;    <span class="keywordtype">bool</span> singular_values_sorted = (((singVals.segment(1,actual_n-1)-singVals.head(actual_n-1))).array() &gt;= 0).<a class="code" href="group__Core__Module.html#ga4abe6022fbef6cda264ef2947a2be1a9">all</a>();</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;    <span class="keywordflow">if</span>(!singular_values_sorted)</div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;      std::cout &lt;&lt; <span class="stringliteral">&quot;Singular values are not sorted: &quot;</span> &lt;&lt; singVals.segment(1,actual_n).transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;    assert(singular_values_sorted);</div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;  }</div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160; </div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;  <span class="comment">// Reverse order so that singular values in increased order</span></div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160;  <span class="comment">// Because of deflation, the zeros singular-values are already at the end</span></div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;  singVals.head(actual_n).reverseInPlace();</div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;  U.leftCols(actual_n).rowwise().reverseInPlace();</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;  <span class="keywordflow">if</span> (m_compV) V.leftCols(actual_n).rowwise().reverseInPlace();</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160; </div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;  JacobiSVD&lt;MatrixXr&gt; jsvd(m_computed.block(firstCol, firstCol, n, n) );</div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  * j:        &quot;</span> &lt;&lt; jsvd.singularValues().transpose() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;  * sing-val: &quot;</span> &lt;&lt; singVals.transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;<span class="comment">//   std::cout &lt;&lt; &quot;  * err:      &quot; &lt;&lt; ((jsvd.singularValues()-singVals)&gt;1e-13*singVals.norm()).transpose() &lt;&lt; &quot;\n&quot;;</span></div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;}</div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160; </div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;<span class="keyword">typename</span> BDCSVD&lt;MatrixType, Options&gt;::RealScalar BDCSVD&lt;MatrixType, Options&gt;::secularEq(</div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;    RealScalar mu, <span class="keyword">const</span> ArrayRef&amp; col0, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef&amp; perm, <span class="keyword">const</span> ArrayRef&amp; diagShifted,</div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;    RealScalar shift) {</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = perm.size();</div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;  RealScalar res = Literal(1);</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=0; i&lt;m; ++i)</div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;  {</div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = perm(i);</div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;    <span class="comment">// The following expression could be rewritten to involve only a single division,</span></div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;    <span class="comment">// but this would make the expression more sensitive to overflow.</span></div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;    res += (col0(j) / (diagShifted(j) - mu)) * (col0(j) / (diag(j) + shift + mu));</div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;  }</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;}</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160; </div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::computeSingVals(<span class="keyword">const</span> ArrayRef&amp; col0, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef&amp; perm,</div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;                                                  VectorType&amp; singVals, ArrayRef shifts, ArrayRef mus) {</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;  <span class="keyword">using</span> std::swap;</div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160; </div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = col0.size();</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> actual_n = n;</div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160;  <span class="comment">// Note that here actual_n is computed based on col0(i)==0 instead of diag(i)==0 as above</span></div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;  <span class="comment">// because 1) we have diag(i)==0 =&gt; col0(i)==0 and 2) if col0(i)==0, then diag(i) is already a singular value.</span></div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;  <span class="keywordflow">while</span>(actual_n&gt;1 &amp;&amp; numext::is_exactly_zero(col0(actual_n - 1))) --actual_n;</div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160; </div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; n; ++k)</div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;  {</div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;    <span class="keywordflow">if</span> (numext::is_exactly_zero(col0(k)) || actual_n == 1)</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;    {</div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;      <span class="comment">// if col0(k) == 0, then entry is deflated, so singular value is on diagonal</span></div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;      <span class="comment">// if actual_n==1, then the deflated problem is already diagonalized</span></div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160;      singVals(k) = k==0 ? col0(0) : diag(k);</div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;      mus(k) = Literal(0);</div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;      shifts(k) = k==0 ? col0(0) : diag(k);</div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;      <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;    }</div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160; </div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160;    <span class="comment">// otherwise, use secular equation to find singular value</span></div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;    RealScalar left = diag(k);</div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;    RealScalar right; <span class="comment">// was: = (k != actual_n-1) ? diag(k+1) : (diag(actual_n-1) + col0.matrix().norm());</span></div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;    <span class="keywordflow">if</span>(k==actual_n-1)</div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;      right = (diag(actual_n-1) + col0.matrix().norm());</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00835"></a><span class="lineno">  835</span>&#160;    {</div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;      <span class="comment">// Skip deflated singular values,</span></div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;      <span class="comment">// recall that at this stage we assume that z[j]!=0 and all entries for which z[j]==0 have been put aside.</span></div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;      <span class="comment">// This should be equivalent to using perm[]</span></div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> l = k+1;</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;      <span class="keywordflow">while</span>(numext::is_exactly_zero(col0(l))) { ++l; eigen_internal_assert(l &lt; actual_n); }</div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;      right = diag(l);</div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;    }</div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160; </div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;    <span class="comment">// first decide whether it&#39;s closer to the left end or the right end</span></div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;    RealScalar mid = left + (right-left) / Literal(2);</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160;    RealScalar fMid = secularEq(mid, col0, diag, perm, diag, Literal(0));</div>
<div class="line"><a name="l00847"></a><span class="lineno">  847</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;    std::cout &lt;&lt; <span class="stringliteral">&quot;right-left = &quot;</span> &lt;&lt; right-left &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;<span class="comment">//     std::cout &lt;&lt; &quot;fMid = &quot; &lt;&lt; fMid &lt;&lt; &quot; &quot; &lt;&lt; secularEq(mid-left, col0, diag, perm, ArrayXr(diag-left), left)</span></div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;<span class="comment">//                            &lt;&lt; &quot; &quot; &lt;&lt; secularEq(mid-right, col0, diag, perm, ArrayXr(diag-right), right)   &lt;&lt; &quot;\n&quot;;</span></div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;    std::cout &lt;&lt; <span class="stringliteral">&quot;     = &quot;</span> &lt;&lt; secularEq(left+RealScalar(0.000001)*(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.1)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.2)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.3)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.4)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.49)    *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.5)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.51)    *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.6)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00860"></a><span class="lineno">  860</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.7)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.8)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.9)     *(right-left), col0, diag, perm, diag, 0)</div>
<div class="line"><a name="l00863"></a><span class="lineno">  863</span>&#160;              &lt;&lt; <span class="stringliteral">&quot; &quot;</span>       &lt;&lt; secularEq(left+RealScalar(0.999999)*(right-left), col0, diag, perm, diag, 0) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00864"></a><span class="lineno">  864</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;    RealScalar shift = (k == actual_n-1 || fMid &gt; Literal(0)) ? left : right;</div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160; </div>
<div class="line"><a name="l00867"></a><span class="lineno">  867</span>&#160;    <span class="comment">// measure everything relative to shift</span></div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;    Map&lt;ArrayXr&gt; diagShifted(m_workspace.data()+4*n, n);</div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;    diagShifted = diag - shift;</div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160; </div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160;    <span class="keywordflow">if</span>(k!=actual_n-1)</div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160;    {</div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160;      <span class="comment">// check that after the shift, f(mid) is still negative:</span></div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;      RealScalar midShifted = (right - left) / RealScalar(2);</div>
<div class="line"><a name="l00875"></a><span class="lineno">  875</span>&#160;      <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a name="l00876"></a><span class="lineno">  876</span>&#160;      <span class="keywordflow">if</span>(numext::equal_strict(shift, right))</div>
<div class="line"><a name="l00877"></a><span class="lineno">  877</span>&#160;        midShifted = -midShifted;</div>
<div class="line"><a name="l00878"></a><span class="lineno">  878</span>&#160;      RealScalar fMidShifted = secularEq(midShifted, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a name="l00879"></a><span class="lineno">  879</span>&#160;      <span class="keywordflow">if</span>(fMidShifted&gt;0)</div>
<div class="line"><a name="l00880"></a><span class="lineno">  880</span>&#160;      {</div>
<div class="line"><a name="l00881"></a><span class="lineno">  881</span>&#160;        <span class="comment">// fMid was erroneous, fix it:</span></div>
<div class="line"><a name="l00882"></a><span class="lineno">  882</span>&#160;        shift =  fMidShifted &gt; Literal(0) ? left : right;</div>
<div class="line"><a name="l00883"></a><span class="lineno">  883</span>&#160;        diagShifted = diag - shift;</div>
<div class="line"><a name="l00884"></a><span class="lineno">  884</span>&#160;      }</div>
<div class="line"><a name="l00885"></a><span class="lineno">  885</span>&#160;    }</div>
<div class="line"><a name="l00886"></a><span class="lineno">  886</span>&#160; </div>
<div class="line"><a name="l00887"></a><span class="lineno">  887</span>&#160;    <span class="comment">// initial guess</span></div>
<div class="line"><a name="l00888"></a><span class="lineno">  888</span>&#160;    RealScalar muPrev, muCur;</div>
<div class="line"><a name="l00889"></a><span class="lineno">  889</span>&#160;    <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a name="l00890"></a><span class="lineno">  890</span>&#160;    <span class="keywordflow">if</span> (numext::equal_strict(shift, left))</div>
<div class="line"><a name="l00891"></a><span class="lineno">  891</span>&#160;    {</div>
<div class="line"><a name="l00892"></a><span class="lineno">  892</span>&#160;      muPrev = (right - left) * RealScalar(0.1);</div>
<div class="line"><a name="l00893"></a><span class="lineno">  893</span>&#160;      <span class="keywordflow">if</span> (k == actual_n-1) muCur = right - left;</div>
<div class="line"><a name="l00894"></a><span class="lineno">  894</span>&#160;      <span class="keywordflow">else</span>                 muCur = (right - left) * RealScalar(0.5);</div>
<div class="line"><a name="l00895"></a><span class="lineno">  895</span>&#160;    }</div>
<div class="line"><a name="l00896"></a><span class="lineno">  896</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00897"></a><span class="lineno">  897</span>&#160;    {</div>
<div class="line"><a name="l00898"></a><span class="lineno">  898</span>&#160;      muPrev = -(right - left) * RealScalar(0.1);</div>
<div class="line"><a name="l00899"></a><span class="lineno">  899</span>&#160;      muCur = -(right - left) * RealScalar(0.5);</div>
<div class="line"><a name="l00900"></a><span class="lineno">  900</span>&#160;    }</div>
<div class="line"><a name="l00901"></a><span class="lineno">  901</span>&#160; </div>
<div class="line"><a name="l00902"></a><span class="lineno">  902</span>&#160;    RealScalar fPrev = secularEq(muPrev, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a name="l00903"></a><span class="lineno">  903</span>&#160;    RealScalar fCur = secularEq(muCur, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a name="l00904"></a><span class="lineno">  904</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(fPrev) &lt; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(fCur))</div>
<div class="line"><a name="l00905"></a><span class="lineno">  905</span>&#160;    {</div>
<div class="line"><a name="l00906"></a><span class="lineno">  906</span>&#160;      swap(fPrev, fCur);</div>
<div class="line"><a name="l00907"></a><span class="lineno">  907</span>&#160;      swap(muPrev, muCur);</div>
<div class="line"><a name="l00908"></a><span class="lineno">  908</span>&#160;    }</div>
<div class="line"><a name="l00909"></a><span class="lineno">  909</span>&#160; </div>
<div class="line"><a name="l00910"></a><span class="lineno">  910</span>&#160;    <span class="comment">// rational interpolation: fit a function of the form a / mu + b through the two previous</span></div>
<div class="line"><a name="l00911"></a><span class="lineno">  911</span>&#160;    <span class="comment">// iterates and use its zero to compute the next iterate</span></div>
<div class="line"><a name="l00912"></a><span class="lineno">  912</span>&#160;    <span class="keywordtype">bool</span> useBisection = fPrev*fCur&gt;Literal(0);</div>
<div class="line"><a name="l00913"></a><span class="lineno">  913</span>&#160;    <span class="keywordflow">while</span> (!numext::is_exactly_zero(fCur) &amp;&amp; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(muCur - muPrev) &gt; Literal(8) * NumTraits&lt;RealScalar&gt;::epsilon() * numext::maxi&lt;RealScalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(muCur), <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(muPrev)) &amp;&amp; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(fCur - fPrev) &gt; NumTraits&lt;RealScalar&gt;::epsilon() &amp;&amp; !useBisection)</div>
<div class="line"><a name="l00914"></a><span class="lineno">  914</span>&#160;    {</div>
<div class="line"><a name="l00915"></a><span class="lineno">  915</span>&#160;      ++m_numIters;</div>
<div class="line"><a name="l00916"></a><span class="lineno">  916</span>&#160; </div>
<div class="line"><a name="l00917"></a><span class="lineno">  917</span>&#160;      <span class="comment">// Find a and b such that the function f(mu) = a / mu + b matches the current and previous samples.</span></div>
<div class="line"><a name="l00918"></a><span class="lineno">  918</span>&#160;      RealScalar a = (fCur - fPrev) / (Literal(1)/muCur - Literal(1)/muPrev);</div>
<div class="line"><a name="l00919"></a><span class="lineno">  919</span>&#160;      RealScalar b = fCur - a / muCur;</div>
<div class="line"><a name="l00920"></a><span class="lineno">  920</span>&#160;      <span class="comment">// And find mu such that f(mu)==0:</span></div>
<div class="line"><a name="l00921"></a><span class="lineno">  921</span>&#160;      RealScalar muZero = -a/b;</div>
<div class="line"><a name="l00922"></a><span class="lineno">  922</span>&#160;      RealScalar fZero = secularEq(muZero, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a name="l00923"></a><span class="lineno">  923</span>&#160; </div>
<div class="line"><a name="l00924"></a><span class="lineno">  924</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00925"></a><span class="lineno">  925</span>&#160;      assert((numext::isfinite)(fZero));</div>
<div class="line"><a name="l00926"></a><span class="lineno">  926</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00927"></a><span class="lineno">  927</span>&#160; </div>
<div class="line"><a name="l00928"></a><span class="lineno">  928</span>&#160;      muPrev = muCur;</div>
<div class="line"><a name="l00929"></a><span class="lineno">  929</span>&#160;      fPrev = fCur;</div>
<div class="line"><a name="l00930"></a><span class="lineno">  930</span>&#160;      muCur = muZero;</div>
<div class="line"><a name="l00931"></a><span class="lineno">  931</span>&#160;      fCur = fZero;</div>
<div class="line"><a name="l00932"></a><span class="lineno">  932</span>&#160; </div>
<div class="line"><a name="l00933"></a><span class="lineno">  933</span>&#160;      <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a name="l00934"></a><span class="lineno">  934</span>&#160;      <span class="keywordflow">if</span> (numext::equal_strict(shift, left)  &amp;&amp; (muCur &lt; Literal(0) || muCur &gt; right - left)) useBisection = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00935"></a><span class="lineno">  935</span>&#160;      <span class="keywordflow">if</span> (numext::equal_strict(shift, right) &amp;&amp; (muCur &lt; -(right - left) || muCur &gt; Literal(0))) useBisection = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00936"></a><span class="lineno">  936</span>&#160;      <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(fCur)&gt;<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(fPrev)) useBisection = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00937"></a><span class="lineno">  937</span>&#160;    }</div>
<div class="line"><a name="l00938"></a><span class="lineno">  938</span>&#160; </div>
<div class="line"><a name="l00939"></a><span class="lineno">  939</span>&#160;    <span class="comment">// fall back on bisection method if rational interpolation did not work</span></div>
<div class="line"><a name="l00940"></a><span class="lineno">  940</span>&#160;    <span class="keywordflow">if</span> (useBisection)</div>
<div class="line"><a name="l00941"></a><span class="lineno">  941</span>&#160;    {</div>
<div class="line"><a name="l00942"></a><span class="lineno">  942</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00943"></a><span class="lineno">  943</span>&#160;      std::cout &lt;&lt; <span class="stringliteral">&quot;useBisection for k = &quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;, actual_n = &quot;</span> &lt;&lt; actual_n &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00944"></a><span class="lineno">  944</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00945"></a><span class="lineno">  945</span>&#160;      RealScalar leftShifted, rightShifted;</div>
<div class="line"><a name="l00946"></a><span class="lineno">  946</span>&#160;      <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a name="l00947"></a><span class="lineno">  947</span>&#160;      <span class="keywordflow">if</span> (numext::equal_strict(shift, left))</div>
<div class="line"><a name="l00948"></a><span class="lineno">  948</span>&#160;      {</div>
<div class="line"><a name="l00949"></a><span class="lineno">  949</span>&#160;        <span class="comment">// to avoid overflow, we must have mu &gt; max(real_min, |z(k)|/sqrt(real_max)),</span></div>
<div class="line"><a name="l00950"></a><span class="lineno">  950</span>&#160;        <span class="comment">// the factor 2 is to be more conservative</span></div>
<div class="line"><a name="l00951"></a><span class="lineno">  951</span>&#160;        leftShifted = numext::maxi&lt;RealScalar&gt;( (std::numeric_limits&lt;RealScalar&gt;::min)(), Literal(2) * <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(col0(k)) / <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>((std::numeric_limits&lt;RealScalar&gt;::max)()) );</div>
<div class="line"><a name="l00952"></a><span class="lineno">  952</span>&#160; </div>
<div class="line"><a name="l00953"></a><span class="lineno">  953</span>&#160;        <span class="comment">// check that we did it right:</span></div>
<div class="line"><a name="l00954"></a><span class="lineno">  954</span>&#160;        eigen_internal_assert( (numext::isfinite)( (col0(k)/leftShifted)*(col0(k)/(diag(k)+shift+leftShifted)) ) );</div>
<div class="line"><a name="l00955"></a><span class="lineno">  955</span>&#160;        <span class="comment">// I don&#39;t understand why the case k==0 would be special there:</span></div>
<div class="line"><a name="l00956"></a><span class="lineno">  956</span>&#160;        <span class="comment">// if (k == 0) rightShifted = right - left; else</span></div>
<div class="line"><a name="l00957"></a><span class="lineno">  957</span>&#160;        rightShifted = (k==actual_n-1) ? right : ((right - left) * RealScalar(0.51)); <span class="comment">// theoretically we can take 0.5, but let&#39;s be safe</span></div>
<div class="line"><a name="l00958"></a><span class="lineno">  958</span>&#160;      }</div>
<div class="line"><a name="l00959"></a><span class="lineno">  959</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l00960"></a><span class="lineno">  960</span>&#160;      {</div>
<div class="line"><a name="l00961"></a><span class="lineno">  961</span>&#160;        leftShifted = -(right - left) * RealScalar(0.51);</div>
<div class="line"><a name="l00962"></a><span class="lineno">  962</span>&#160;        <span class="keywordflow">if</span>(k+1&lt;n)</div>
<div class="line"><a name="l00963"></a><span class="lineno">  963</span>&#160;          rightShifted = -numext::maxi&lt;RealScalar&gt;( (std::numeric_limits&lt;RealScalar&gt;::min)(), <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(col0(k+1)) / <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>((std::numeric_limits&lt;RealScalar&gt;::max)()) );</div>
<div class="line"><a name="l00964"></a><span class="lineno">  964</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l00965"></a><span class="lineno">  965</span>&#160;          rightShifted = -(std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00966"></a><span class="lineno">  966</span>&#160;      }</div>
<div class="line"><a name="l00967"></a><span class="lineno">  967</span>&#160; </div>
<div class="line"><a name="l00968"></a><span class="lineno">  968</span>&#160;      RealScalar fLeft = secularEq(leftShifted, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a name="l00969"></a><span class="lineno">  969</span>&#160;      eigen_internal_assert(fLeft&lt;Literal(0));</div>
<div class="line"><a name="l00970"></a><span class="lineno">  970</span>&#160; </div>
<div class="line"><a name="l00971"></a><span class="lineno">  971</span>&#160;<span class="preprocessor">#if defined EIGEN_BDCSVD_DEBUG_VERBOSE || defined EIGEN_BDCSVD_SANITY_CHECKS || defined EIGEN_INTERNAL_DEBUGGING</span></div>
<div class="line"><a name="l00972"></a><span class="lineno">  972</span>&#160;      RealScalar fRight = secularEq(rightShifted, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a name="l00973"></a><span class="lineno">  973</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00974"></a><span class="lineno">  974</span>&#160; </div>
<div class="line"><a name="l00975"></a><span class="lineno">  975</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l00976"></a><span class="lineno">  976</span>&#160;      <span class="keywordflow">if</span>(!(numext::isfinite)(fLeft))</div>
<div class="line"><a name="l00977"></a><span class="lineno">  977</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;f(&quot;</span> &lt;&lt; leftShifted &lt;&lt; <span class="stringliteral">&quot;) =&quot;</span> &lt;&lt; fLeft &lt;&lt; <span class="stringliteral">&quot; ; &quot;</span> &lt;&lt; left &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; shift &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; right &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00978"></a><span class="lineno">  978</span>&#160;      assert((numext::isfinite)(fLeft));</div>
<div class="line"><a name="l00979"></a><span class="lineno">  979</span>&#160; </div>
<div class="line"><a name="l00980"></a><span class="lineno">  980</span>&#160;      <span class="keywordflow">if</span>(!(numext::isfinite)(fRight))</div>
<div class="line"><a name="l00981"></a><span class="lineno">  981</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;f(&quot;</span> &lt;&lt; rightShifted &lt;&lt; <span class="stringliteral">&quot;) =&quot;</span> &lt;&lt; fRight &lt;&lt; <span class="stringliteral">&quot; ; &quot;</span> &lt;&lt; left &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; shift &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; right &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00982"></a><span class="lineno">  982</span>&#160;      <span class="comment">// assert((numext::isfinite)(fRight));</span></div>
<div class="line"><a name="l00983"></a><span class="lineno">  983</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00984"></a><span class="lineno">  984</span>&#160; </div>
<div class="line"><a name="l00985"></a><span class="lineno">  985</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l00986"></a><span class="lineno">  986</span>&#160;      <span class="keywordflow">if</span>(!(fLeft * fRight&lt;0))</div>
<div class="line"><a name="l00987"></a><span class="lineno">  987</span>&#160;      {</div>
<div class="line"><a name="l00988"></a><span class="lineno">  988</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;f(leftShifted) using  leftShifted=&quot;</span> &lt;&lt; leftShifted &lt;&lt; <span class="stringliteral">&quot; ;  diagShifted(1:10):&quot;</span> &lt;&lt; diagShifted.head(10).transpose()  &lt;&lt; <span class="stringliteral">&quot;\n ; &quot;</span></div>
<div class="line"><a name="l00989"></a><span class="lineno">  989</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;left==shift=&quot;</span> &lt;&lt; bool(left==shift) &lt;&lt; <span class="stringliteral">&quot; ; left-shift = &quot;</span> &lt;&lt; (left-shift) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00990"></a><span class="lineno">  990</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;k=&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;, &quot;</span> &lt;&lt;  fLeft &lt;&lt; <span class="stringliteral">&quot; * &quot;</span> &lt;&lt; fRight &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; fLeft * fRight &lt;&lt; <span class="stringliteral">&quot;  ;  &quot;</span></div>
<div class="line"><a name="l00991"></a><span class="lineno">  991</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot;[&quot;</span> &lt;&lt; left &lt;&lt; <span class="stringliteral">&quot; .. &quot;</span> &lt;&lt; right &lt;&lt; <span class="stringliteral">&quot;] -&gt; [&quot;</span> &lt;&lt; leftShifted &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; rightShifted &lt;&lt; <span class="stringliteral">&quot;], shift=&quot;</span> &lt;&lt; shift</div>
<div class="line"><a name="l00992"></a><span class="lineno">  992</span>&#160;                  &lt;&lt; <span class="stringliteral">&quot; ,  f(right)=&quot;</span> &lt;&lt; secularEq(0,     col0, diag, perm, diagShifted, shift)</div>
<div class="line"><a name="l00993"></a><span class="lineno">  993</span>&#160;                           &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; secularEq(right, col0, diag, perm, diag, 0) &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; fRight &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00994"></a><span class="lineno">  994</span>&#160;      }</div>
<div class="line"><a name="l00995"></a><span class="lineno">  995</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00996"></a><span class="lineno">  996</span>&#160;      eigen_internal_assert(fLeft * fRight &lt; Literal(0));</div>
<div class="line"><a name="l00997"></a><span class="lineno">  997</span>&#160; </div>
<div class="line"><a name="l00998"></a><span class="lineno">  998</span>&#160;      <span class="keywordflow">if</span>(fLeft&lt;Literal(0))</div>
<div class="line"><a name="l00999"></a><span class="lineno">  999</span>&#160;      {</div>
<div class="line"><a name="l01000"></a><span class="lineno"> 1000</span>&#160;        <span class="keywordflow">while</span> (rightShifted - leftShifted &gt; Literal(2) * NumTraits&lt;RealScalar&gt;::epsilon() * numext::maxi&lt;RealScalar&gt;(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(leftShifted), <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(rightShifted)))</div>
<div class="line"><a name="l01001"></a><span class="lineno"> 1001</span>&#160;        {</div>
<div class="line"><a name="l01002"></a><span class="lineno"> 1002</span>&#160;          RealScalar midShifted = (leftShifted + rightShifted) / Literal(2);</div>
<div class="line"><a name="l01003"></a><span class="lineno"> 1003</span>&#160;          fMid = secularEq(midShifted, col0, diag, perm, diagShifted, shift);</div>
<div class="line"><a name="l01004"></a><span class="lineno"> 1004</span>&#160;          eigen_internal_assert((numext::isfinite)(fMid));</div>
<div class="line"><a name="l01005"></a><span class="lineno"> 1005</span>&#160; </div>
<div class="line"><a name="l01006"></a><span class="lineno"> 1006</span>&#160;          <span class="keywordflow">if</span> (fLeft * fMid &lt; Literal(0))</div>
<div class="line"><a name="l01007"></a><span class="lineno"> 1007</span>&#160;          {</div>
<div class="line"><a name="l01008"></a><span class="lineno"> 1008</span>&#160;            rightShifted = midShifted;</div>
<div class="line"><a name="l01009"></a><span class="lineno"> 1009</span>&#160;          }</div>
<div class="line"><a name="l01010"></a><span class="lineno"> 1010</span>&#160;          <span class="keywordflow">else</span></div>
<div class="line"><a name="l01011"></a><span class="lineno"> 1011</span>&#160;          {</div>
<div class="line"><a name="l01012"></a><span class="lineno"> 1012</span>&#160;            leftShifted = midShifted;</div>
<div class="line"><a name="l01013"></a><span class="lineno"> 1013</span>&#160;            fLeft = fMid;</div>
<div class="line"><a name="l01014"></a><span class="lineno"> 1014</span>&#160;          }</div>
<div class="line"><a name="l01015"></a><span class="lineno"> 1015</span>&#160;        }</div>
<div class="line"><a name="l01016"></a><span class="lineno"> 1016</span>&#160;        muCur = (leftShifted + rightShifted) / Literal(2);</div>
<div class="line"><a name="l01017"></a><span class="lineno"> 1017</span>&#160;      }</div>
<div class="line"><a name="l01018"></a><span class="lineno"> 1018</span>&#160;      <span class="keywordflow">else</span></div>
<div class="line"><a name="l01019"></a><span class="lineno"> 1019</span>&#160;      {</div>
<div class="line"><a name="l01020"></a><span class="lineno"> 1020</span>&#160;        <span class="comment">// We have a problem as shifting on the left or right give either a positive or negative value</span></div>
<div class="line"><a name="l01021"></a><span class="lineno"> 1021</span>&#160;        <span class="comment">// at the middle of [left,right]...</span></div>
<div class="line"><a name="l01022"></a><span class="lineno"> 1022</span>&#160;        <span class="comment">// Instead fo abbording or entering an infinite loop,</span></div>
<div class="line"><a name="l01023"></a><span class="lineno"> 1023</span>&#160;        <span class="comment">// let&#39;s just use the middle as the estimated zero-crossing:</span></div>
<div class="line"><a name="l01024"></a><span class="lineno"> 1024</span>&#160;        muCur = (right - left) * RealScalar(0.5);</div>
<div class="line"><a name="l01025"></a><span class="lineno"> 1025</span>&#160;        <span class="comment">// we can test exact equality here, because shift comes from `... ? left : right`</span></div>
<div class="line"><a name="l01026"></a><span class="lineno"> 1026</span>&#160;        <span class="keywordflow">if</span>(numext::equal_strict(shift, right))</div>
<div class="line"><a name="l01027"></a><span class="lineno"> 1027</span>&#160;          muCur = -muCur;</div>
<div class="line"><a name="l01028"></a><span class="lineno"> 1028</span>&#160;      }</div>
<div class="line"><a name="l01029"></a><span class="lineno"> 1029</span>&#160;    }</div>
<div class="line"><a name="l01030"></a><span class="lineno"> 1030</span>&#160; </div>
<div class="line"><a name="l01031"></a><span class="lineno"> 1031</span>&#160;    singVals[k] = shift + muCur;</div>
<div class="line"><a name="l01032"></a><span class="lineno"> 1032</span>&#160;    shifts[k] = shift;</div>
<div class="line"><a name="l01033"></a><span class="lineno"> 1033</span>&#160;    mus[k] = muCur;</div>
<div class="line"><a name="l01034"></a><span class="lineno"> 1034</span>&#160; </div>
<div class="line"><a name="l01035"></a><span class="lineno"> 1035</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01036"></a><span class="lineno"> 1036</span>&#160;    <span class="keywordflow">if</span>(k+1&lt;n)</div>
<div class="line"><a name="l01037"></a><span class="lineno"> 1037</span>&#160;      std::cout &lt;&lt; <span class="stringliteral">&quot;found &quot;</span> &lt;&lt; singVals[k] &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; shift &lt;&lt; <span class="stringliteral">&quot; + &quot;</span> &lt;&lt; muCur &lt;&lt; <span class="stringliteral">&quot; from &quot;</span> &lt;&lt; diag(k) &lt;&lt; <span class="stringliteral">&quot; .. &quot;</span>  &lt;&lt; diag(k+1) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01038"></a><span class="lineno"> 1038</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01039"></a><span class="lineno"> 1039</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01040"></a><span class="lineno"> 1040</span>&#160;    assert(k==0 || singVals[k]&gt;=singVals[k-1]);</div>
<div class="line"><a name="l01041"></a><span class="lineno"> 1041</span>&#160;    assert(singVals[k]&gt;=diag(k));</div>
<div class="line"><a name="l01042"></a><span class="lineno"> 1042</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01043"></a><span class="lineno"> 1043</span>&#160; </div>
<div class="line"><a name="l01044"></a><span class="lineno"> 1044</span>&#160;    <span class="comment">// perturb singular value slightly if it equals diagonal entry to avoid division by zero later</span></div>
<div class="line"><a name="l01045"></a><span class="lineno"> 1045</span>&#160;    <span class="comment">// (deflation is supposed to avoid this from happening)</span></div>
<div class="line"><a name="l01046"></a><span class="lineno"> 1046</span>&#160;    <span class="comment">// - this does no seem to be necessary anymore -</span></div>
<div class="line"><a name="l01047"></a><span class="lineno"> 1047</span>&#160;<span class="comment">//     if (singVals[k] == left) singVals[k] *= 1 + NumTraits&lt;RealScalar&gt;::epsilon();</span></div>
<div class="line"><a name="l01048"></a><span class="lineno"> 1048</span>&#160;<span class="comment">//     if (singVals[k] == right) singVals[k] *= 1 - NumTraits&lt;RealScalar&gt;::epsilon();</span></div>
<div class="line"><a name="l01049"></a><span class="lineno"> 1049</span>&#160;  }</div>
<div class="line"><a name="l01050"></a><span class="lineno"> 1050</span>&#160;}</div>
<div class="line"><a name="l01051"></a><span class="lineno"> 1051</span>&#160; </div>
<div class="line"><a name="l01052"></a><span class="lineno"> 1052</span>&#160;<span class="comment">// zhat is perturbation of col0 for which singular vectors can be computed stably (see Section 3.1)</span></div>
<div class="line"><a name="l01053"></a><span class="lineno"> 1053</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l01054"></a><span class="lineno"> 1054</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::perturbCol0(<span class="keyword">const</span> ArrayRef&amp; col0, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef&amp; perm,</div>
<div class="line"><a name="l01055"></a><span class="lineno"> 1055</span>&#160;                                              <span class="keyword">const</span> VectorType&amp; singVals, <span class="keyword">const</span> ArrayRef&amp; shifts, <span class="keyword">const</span> ArrayRef&amp; mus,</div>
<div class="line"><a name="l01056"></a><span class="lineno"> 1056</span>&#160;                                              ArrayRef zhat) {</div>
<div class="line"><a name="l01057"></a><span class="lineno"> 1057</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l01058"></a><span class="lineno"> 1058</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = col0.size();</div>
<div class="line"><a name="l01059"></a><span class="lineno"> 1059</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = perm.size();</div>
<div class="line"><a name="l01060"></a><span class="lineno"> 1060</span>&#160;  <span class="keywordflow">if</span>(m==0)</div>
<div class="line"><a name="l01061"></a><span class="lineno"> 1061</span>&#160;  {</div>
<div class="line"><a name="l01062"></a><span class="lineno"> 1062</span>&#160;    zhat.setZero();</div>
<div class="line"><a name="l01063"></a><span class="lineno"> 1063</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l01064"></a><span class="lineno"> 1064</span>&#160;  }</div>
<div class="line"><a name="l01065"></a><span class="lineno"> 1065</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> lastIdx = perm(m-1);</div>
<div class="line"><a name="l01066"></a><span class="lineno"> 1066</span>&#160;  <span class="comment">// The offset permits to skip deflated entries while computing zhat</span></div>
<div class="line"><a name="l01067"></a><span class="lineno"> 1067</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; n; ++k)</div>
<div class="line"><a name="l01068"></a><span class="lineno"> 1068</span>&#160;  {</div>
<div class="line"><a name="l01069"></a><span class="lineno"> 1069</span>&#160;    <span class="keywordflow">if</span> (numext::is_exactly_zero(col0(k))) <span class="comment">// deflated</span></div>
<div class="line"><a name="l01070"></a><span class="lineno"> 1070</span>&#160;      zhat(k) = Literal(0);</div>
<div class="line"><a name="l01071"></a><span class="lineno"> 1071</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l01072"></a><span class="lineno"> 1072</span>&#160;    {</div>
<div class="line"><a name="l01073"></a><span class="lineno"> 1073</span>&#160;      <span class="comment">// see equation (3.6)</span></div>
<div class="line"><a name="l01074"></a><span class="lineno"> 1074</span>&#160;      RealScalar dk = diag(k);</div>
<div class="line"><a name="l01075"></a><span class="lineno"> 1075</span>&#160;      RealScalar prod = (singVals(lastIdx) + dk) * (mus(lastIdx) + (shifts(lastIdx) - dk));</div>
<div class="line"><a name="l01076"></a><span class="lineno"> 1076</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01077"></a><span class="lineno"> 1077</span>&#160;      <span class="keywordflow">if</span>(prod&lt;0) {</div>
<div class="line"><a name="l01078"></a><span class="lineno"> 1078</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;k = &quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot; ;  z(k)=&quot;</span> &lt;&lt; col0(k) &lt;&lt; <span class="stringliteral">&quot;, diag(k)=&quot;</span> &lt;&lt; dk &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01079"></a><span class="lineno"> 1079</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;prod = &quot;</span> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; singVals(lastIdx) &lt;&lt; <span class="stringliteral">&quot; + &quot;</span> &lt;&lt; dk &lt;&lt; <span class="stringliteral">&quot;) * (&quot;</span> &lt;&lt; mus(lastIdx) &lt;&lt; <span class="stringliteral">&quot; + (&quot;</span> &lt;&lt; shifts(lastIdx) &lt;&lt; <span class="stringliteral">&quot; - &quot;</span> &lt;&lt; dk &lt;&lt; <span class="stringliteral">&quot;))&quot;</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01080"></a><span class="lineno"> 1080</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;     = &quot;</span> &lt;&lt; singVals(lastIdx) + dk &lt;&lt; <span class="stringliteral">&quot; * &quot;</span> &lt;&lt; mus(lastIdx) + (shifts(lastIdx) - dk) &lt;&lt;  <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01081"></a><span class="lineno"> 1081</span>&#160;      }</div>
<div class="line"><a name="l01082"></a><span class="lineno"> 1082</span>&#160;      assert(prod&gt;=0);</div>
<div class="line"><a name="l01083"></a><span class="lineno"> 1083</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01084"></a><span class="lineno"> 1084</span>&#160; </div>
<div class="line"><a name="l01085"></a><span class="lineno"> 1085</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> l = 0; l&lt;m; ++l)</div>
<div class="line"><a name="l01086"></a><span class="lineno"> 1086</span>&#160;      {</div>
<div class="line"><a name="l01087"></a><span class="lineno"> 1087</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = perm(l);</div>
<div class="line"><a name="l01088"></a><span class="lineno"> 1088</span>&#160;        <span class="keywordflow">if</span>(i!=k)</div>
<div class="line"><a name="l01089"></a><span class="lineno"> 1089</span>&#160;        {</div>
<div class="line"><a name="l01090"></a><span class="lineno"> 1090</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01091"></a><span class="lineno"> 1091</span>&#160;          <span class="keywordflow">if</span>(i&gt;=k &amp;&amp; (l==0 || l-1&gt;=m))</div>
<div class="line"><a name="l01092"></a><span class="lineno"> 1092</span>&#160;          {</div>
<div class="line"><a name="l01093"></a><span class="lineno"> 1093</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;Error in perturbCol0\n&quot;</span>;</div>
<div class="line"><a name="l01094"></a><span class="lineno"> 1094</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;  &quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;/&quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; &quot;</span>  &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;/&quot;</span> &lt;&lt; m &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;/&quot;</span> &lt;&lt; n &lt;&lt; <span class="stringliteral">&quot; ; &quot;</span> &lt;&lt; col0(k) &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; diag(k) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>  &lt;&lt;  <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01095"></a><span class="lineno"> 1095</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;  &quot;</span> &lt;&lt;diag(i) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01096"></a><span class="lineno"> 1096</span>&#160;            <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = (i&lt;k <span class="comment">/*|| l==0*/</span>) ? i : perm(l-1);</div>
<div class="line"><a name="l01097"></a><span class="lineno"> 1097</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;  &quot;</span> &lt;&lt; <span class="stringliteral">&quot;j=&quot;</span> &lt;&lt; j &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01098"></a><span class="lineno"> 1098</span>&#160;          }</div>
<div class="line"><a name="l01099"></a><span class="lineno"> 1099</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01100"></a><span class="lineno"> 1100</span>&#160;          <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = i&lt;k ? i : perm(l-1);</div>
<div class="line"><a name="l01101"></a><span class="lineno"> 1101</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01102"></a><span class="lineno"> 1102</span>&#160;          <span class="keywordflow">if</span>(!(dk!=Literal(0) || diag(i)!=Literal(0)))</div>
<div class="line"><a name="l01103"></a><span class="lineno"> 1103</span>&#160;          {</div>
<div class="line"><a name="l01104"></a><span class="lineno"> 1104</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;k=&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;, i=&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;, l=&quot;</span> &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;, perm.size()=&quot;</span> &lt;&lt; perm.size() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01105"></a><span class="lineno"> 1105</span>&#160;          }</div>
<div class="line"><a name="l01106"></a><span class="lineno"> 1106</span>&#160;          assert(dk!=Literal(0) || diag(i)!=Literal(0));</div>
<div class="line"><a name="l01107"></a><span class="lineno"> 1107</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01108"></a><span class="lineno"> 1108</span>&#160;          prod *= ((singVals(j)+dk) / ((diag(i)+dk))) * ((mus(j)+(shifts(j)-dk)) / ((diag(i)-dk)));</div>
<div class="line"><a name="l01109"></a><span class="lineno"> 1109</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01110"></a><span class="lineno"> 1110</span>&#160;          assert(prod&gt;=0);</div>
<div class="line"><a name="l01111"></a><span class="lineno"> 1111</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01112"></a><span class="lineno"> 1112</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01113"></a><span class="lineno"> 1113</span>&#160;          <span class="keywordflow">if</span>(i!=k &amp;&amp; numext::abs(((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) - 1) &gt; 0.9 )</div>
<div class="line"><a name="l01114"></a><span class="lineno"> 1114</span>&#160;            std::cout &lt;&lt; <span class="stringliteral">&quot;     &quot;</span> &lt;&lt; ((singVals(j)+dk)*(mus(j)+(shifts(j)-dk)))/((diag(i)+dk)*(diag(i)-dk)) &lt;&lt; <span class="stringliteral">&quot; == (&quot;</span> &lt;&lt; (singVals(j)+dk) &lt;&lt; <span class="stringliteral">&quot; * &quot;</span> &lt;&lt; (mus(j)+(shifts(j)-dk))</div>
<div class="line"><a name="l01115"></a><span class="lineno"> 1115</span>&#160;                       &lt;&lt; <span class="stringliteral">&quot;) / (&quot;</span> &lt;&lt; (diag(i)+dk) &lt;&lt; <span class="stringliteral">&quot; * &quot;</span> &lt;&lt; (diag(i)-dk) &lt;&lt; <span class="stringliteral">&quot;)\n&quot;</span>;</div>
<div class="line"><a name="l01116"></a><span class="lineno"> 1116</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01117"></a><span class="lineno"> 1117</span>&#160;        }</div>
<div class="line"><a name="l01118"></a><span class="lineno"> 1118</span>&#160;      }</div>
<div class="line"><a name="l01119"></a><span class="lineno"> 1119</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01120"></a><span class="lineno"> 1120</span>&#160;      std::cout &lt;&lt; <span class="stringliteral">&quot;zhat(&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;) =  sqrt( &quot;</span> &lt;&lt; prod &lt;&lt; <span class="stringliteral">&quot;)  ;  &quot;</span> &lt;&lt; (singVals(lastIdx) + dk) &lt;&lt; <span class="stringliteral">&quot; * &quot;</span> &lt;&lt; mus(lastIdx) + shifts(lastIdx) &lt;&lt; <span class="stringliteral">&quot; - &quot;</span> &lt;&lt; dk &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01121"></a><span class="lineno"> 1121</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01122"></a><span class="lineno"> 1122</span>&#160;      RealScalar tmp = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(prod);</div>
<div class="line"><a name="l01123"></a><span class="lineno"> 1123</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01124"></a><span class="lineno"> 1124</span>&#160;      assert((numext::isfinite)(tmp));</div>
<div class="line"><a name="l01125"></a><span class="lineno"> 1125</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01126"></a><span class="lineno"> 1126</span>&#160;      zhat(k) = col0(k) &gt; Literal(0) ? RealScalar(tmp) : RealScalar(-tmp);</div>
<div class="line"><a name="l01127"></a><span class="lineno"> 1127</span>&#160;    }</div>
<div class="line"><a name="l01128"></a><span class="lineno"> 1128</span>&#160;  }</div>
<div class="line"><a name="l01129"></a><span class="lineno"> 1129</span>&#160;}</div>
<div class="line"><a name="l01130"></a><span class="lineno"> 1130</span>&#160; </div>
<div class="line"><a name="l01131"></a><span class="lineno"> 1131</span>&#160;<span class="comment">// compute singular vectors</span></div>
<div class="line"><a name="l01132"></a><span class="lineno"> 1132</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l01133"></a><span class="lineno"> 1133</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::computeSingVecs(<span class="keyword">const</span> ArrayRef&amp; zhat, <span class="keyword">const</span> ArrayRef&amp; diag, <span class="keyword">const</span> IndicesRef&amp; perm,</div>
<div class="line"><a name="l01134"></a><span class="lineno"> 1134</span>&#160;                                                  <span class="keyword">const</span> VectorType&amp; singVals, <span class="keyword">const</span> ArrayRef&amp; shifts,</div>
<div class="line"><a name="l01135"></a><span class="lineno"> 1135</span>&#160;                                                  <span class="keyword">const</span> ArrayRef&amp; mus, MatrixXr&amp; U, MatrixXr&amp; V) {</div>
<div class="line"><a name="l01136"></a><span class="lineno"> 1136</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = zhat.size();</div>
<div class="line"><a name="l01137"></a><span class="lineno"> 1137</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = perm.size();</div>
<div class="line"><a name="l01138"></a><span class="lineno"> 1138</span>&#160; </div>
<div class="line"><a name="l01139"></a><span class="lineno"> 1139</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; n; ++k)</div>
<div class="line"><a name="l01140"></a><span class="lineno"> 1140</span>&#160;  {</div>
<div class="line"><a name="l01141"></a><span class="lineno"> 1141</span>&#160;    <span class="keywordflow">if</span> (numext::is_exactly_zero(zhat(k)))</div>
<div class="line"><a name="l01142"></a><span class="lineno"> 1142</span>&#160;    {</div>
<div class="line"><a name="l01143"></a><span class="lineno"> 1143</span>&#160;      U.col(k) = VectorType::Unit(n+1, k);</div>
<div class="line"><a name="l01144"></a><span class="lineno"> 1144</span>&#160;      <span class="keywordflow">if</span> (m_compV) V.col(k) = VectorType::Unit(n, k);</div>
<div class="line"><a name="l01145"></a><span class="lineno"> 1145</span>&#160;    }</div>
<div class="line"><a name="l01146"></a><span class="lineno"> 1146</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l01147"></a><span class="lineno"> 1147</span>&#160;    {</div>
<div class="line"><a name="l01148"></a><span class="lineno"> 1148</span>&#160;      U.col(k).setZero();</div>
<div class="line"><a name="l01149"></a><span class="lineno"> 1149</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> l=0;l&lt;m;++l)</div>
<div class="line"><a name="l01150"></a><span class="lineno"> 1150</span>&#160;      {</div>
<div class="line"><a name="l01151"></a><span class="lineno"> 1151</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = perm(l);</div>
<div class="line"><a name="l01152"></a><span class="lineno"> 1152</span>&#160;        U(i,k) = zhat(i)/(((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));</div>
<div class="line"><a name="l01153"></a><span class="lineno"> 1153</span>&#160;      }</div>
<div class="line"><a name="l01154"></a><span class="lineno"> 1154</span>&#160;      U(n,k) = Literal(0);</div>
<div class="line"><a name="l01155"></a><span class="lineno"> 1155</span>&#160;      U.col(k).normalize();</div>
<div class="line"><a name="l01156"></a><span class="lineno"> 1156</span>&#160; </div>
<div class="line"><a name="l01157"></a><span class="lineno"> 1157</span>&#160;      <span class="keywordflow">if</span> (m_compV)</div>
<div class="line"><a name="l01158"></a><span class="lineno"> 1158</span>&#160;      {</div>
<div class="line"><a name="l01159"></a><span class="lineno"> 1159</span>&#160;        V.col(k).setZero();</div>
<div class="line"><a name="l01160"></a><span class="lineno"> 1160</span>&#160;        <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> l=1;l&lt;m;++l)</div>
<div class="line"><a name="l01161"></a><span class="lineno"> 1161</span>&#160;        {</div>
<div class="line"><a name="l01162"></a><span class="lineno"> 1162</span>&#160;          <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = perm(l);</div>
<div class="line"><a name="l01163"></a><span class="lineno"> 1163</span>&#160;          V(i,k) = diag(i) * zhat(i) / (((diag(i) - shifts(k)) - mus(k)) )/( (diag(i) + singVals[k]));</div>
<div class="line"><a name="l01164"></a><span class="lineno"> 1164</span>&#160;        }</div>
<div class="line"><a name="l01165"></a><span class="lineno"> 1165</span>&#160;        V(0,k) = Literal(-1);</div>
<div class="line"><a name="l01166"></a><span class="lineno"> 1166</span>&#160;        V.col(k).normalize();</div>
<div class="line"><a name="l01167"></a><span class="lineno"> 1167</span>&#160;      }</div>
<div class="line"><a name="l01168"></a><span class="lineno"> 1168</span>&#160;    }</div>
<div class="line"><a name="l01169"></a><span class="lineno"> 1169</span>&#160;  }</div>
<div class="line"><a name="l01170"></a><span class="lineno"> 1170</span>&#160;  U.col(n) = VectorType::Unit(n+1, n);</div>
<div class="line"><a name="l01171"></a><span class="lineno"> 1171</span>&#160;}</div>
<div class="line"><a name="l01172"></a><span class="lineno"> 1172</span>&#160; </div>
<div class="line"><a name="l01173"></a><span class="lineno"> 1173</span>&#160;<span class="comment">// page 12_13</span></div>
<div class="line"><a name="l01174"></a><span class="lineno"> 1174</span>&#160;<span class="comment">// i &gt;= 1, di almost null and zi non null.</span></div>
<div class="line"><a name="l01175"></a><span class="lineno"> 1175</span>&#160;<span class="comment">// We use a rotation to zero out zi applied to the left of M</span></div>
<div class="line"><a name="l01176"></a><span class="lineno"> 1176</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l01177"></a><span class="lineno"> 1177</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::deflation43(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstCol, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> shift, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i,</div>
<div class="line"><a name="l01178"></a><span class="lineno"> 1178</span>&#160;                                              <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size) {</div>
<div class="line"><a name="l01179"></a><span class="lineno"> 1179</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l01180"></a><span class="lineno"> 1180</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l01181"></a><span class="lineno"> 1181</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l01182"></a><span class="lineno"> 1182</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> start = firstCol + shift;</div>
<div class="line"><a name="l01183"></a><span class="lineno"> 1183</span>&#160;  RealScalar c = m_computed(start, start);</div>
<div class="line"><a name="l01184"></a><span class="lineno"> 1184</span>&#160;  RealScalar s = m_computed(start+i, start);</div>
<div class="line"><a name="l01185"></a><span class="lineno"> 1185</span>&#160;  RealScalar r = numext::hypot(c,s);</div>
<div class="line"><a name="l01186"></a><span class="lineno"> 1186</span>&#160;  <span class="keywordflow">if</span> (numext::is_exactly_zero(r))</div>
<div class="line"><a name="l01187"></a><span class="lineno"> 1187</span>&#160;  {</div>
<div class="line"><a name="l01188"></a><span class="lineno"> 1188</span>&#160;    m_computed(start+i, start+i) = Literal(0);</div>
<div class="line"><a name="l01189"></a><span class="lineno"> 1189</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l01190"></a><span class="lineno"> 1190</span>&#160;  }</div>
<div class="line"><a name="l01191"></a><span class="lineno"> 1191</span>&#160;  m_computed(start,start) = r;</div>
<div class="line"><a name="l01192"></a><span class="lineno"> 1192</span>&#160;  m_computed(start+i, start) = Literal(0);</div>
<div class="line"><a name="l01193"></a><span class="lineno"> 1193</span>&#160;  m_computed(start+i, start+i) = Literal(0);</div>
<div class="line"><a name="l01194"></a><span class="lineno"> 1194</span>&#160; </div>
<div class="line"><a name="l01195"></a><span class="lineno"> 1195</span>&#160;  JacobiRotation&lt;RealScalar&gt; J(c/r,-s/r);</div>
<div class="line"><a name="l01196"></a><span class="lineno"> 1196</span>&#160;  <span class="keywordflow">if</span> (m_compU)  m_naiveU.middleRows(firstCol, size+1).applyOnTheRight(firstCol, firstCol+i, J);</div>
<div class="line"><a name="l01197"></a><span class="lineno"> 1197</span>&#160;  <span class="keywordflow">else</span>          m_naiveU.applyOnTheRight(firstCol, firstCol+i, J);</div>
<div class="line"><a name="l01198"></a><span class="lineno"> 1198</span>&#160;}  <span class="comment">// end deflation 43</span></div>
<div class="line"><a name="l01199"></a><span class="lineno"> 1199</span>&#160; </div>
<div class="line"><a name="l01200"></a><span class="lineno"> 1200</span>&#160;<span class="comment">// page 13</span></div>
<div class="line"><a name="l01201"></a><span class="lineno"> 1201</span>&#160;<span class="comment">// i,j &gt;= 1, i!=j and |di - dj| &lt; epsilon * norm2(M)</span></div>
<div class="line"><a name="l01202"></a><span class="lineno"> 1202</span>&#160;<span class="comment">// We apply two rotations to have zj = 0;</span></div>
<div class="line"><a name="l01203"></a><span class="lineno"> 1203</span>&#160;<span class="comment">// TODO deflation44 is still broken and not properly tested</span></div>
<div class="line"><a name="l01204"></a><span class="lineno"> 1204</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l01205"></a><span class="lineno"> 1205</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::deflation44(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstColu, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstColm, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstRowW,</div>
<div class="line"><a name="l01206"></a><span class="lineno"> 1206</span>&#160;                                              <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstColW, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j,</div>
<div class="line"><a name="l01207"></a><span class="lineno"> 1207</span>&#160;                                              <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size) {</div>
<div class="line"><a name="l01208"></a><span class="lineno"> 1208</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l01209"></a><span class="lineno"> 1209</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l01210"></a><span class="lineno"> 1210</span>&#160;  <span class="keyword">using</span> std::conj;</div>
<div class="line"><a name="l01211"></a><span class="lineno"> 1211</span>&#160;  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l01212"></a><span class="lineno"> 1212</span>&#160;  RealScalar c = m_computed(firstColm+i, firstColm);</div>
<div class="line"><a name="l01213"></a><span class="lineno"> 1213</span>&#160;  RealScalar s = m_computed(firstColm+j, firstColm);</div>
<div class="line"><a name="l01214"></a><span class="lineno"> 1214</span>&#160;  RealScalar r = <a class="code" href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(numext::abs2(c) + numext::abs2(s));</div>
<div class="line"><a name="l01215"></a><span class="lineno"> 1215</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01216"></a><span class="lineno"> 1216</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;deflation 4.4: &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; j &lt;&lt; <span class="stringliteral">&quot; -&gt; &quot;</span> &lt;&lt; c &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; s &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; r &lt;&lt; <span class="stringliteral">&quot; ; &quot;</span></div>
<div class="line"><a name="l01217"></a><span class="lineno"> 1217</span>&#160;    &lt;&lt; m_computed(firstColm + i-1, firstColm)  &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
<div class="line"><a name="l01218"></a><span class="lineno"> 1218</span>&#160;    &lt;&lt; m_computed(firstColm + i, firstColm)  &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
<div class="line"><a name="l01219"></a><span class="lineno"> 1219</span>&#160;    &lt;&lt; m_computed(firstColm + i+1, firstColm) &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
<div class="line"><a name="l01220"></a><span class="lineno"> 1220</span>&#160;    &lt;&lt; m_computed(firstColm + i+2, firstColm) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01221"></a><span class="lineno"> 1221</span>&#160;  std::cout &lt;&lt; m_computed(firstColm + i-1, firstColm + i-1)  &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
<div class="line"><a name="l01222"></a><span class="lineno"> 1222</span>&#160;    &lt;&lt; m_computed(firstColm + i, firstColm+i)  &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
<div class="line"><a name="l01223"></a><span class="lineno"> 1223</span>&#160;    &lt;&lt; m_computed(firstColm + i+1, firstColm+i+1) &lt;&lt; <span class="stringliteral">&quot; &quot;</span></div>
<div class="line"><a name="l01224"></a><span class="lineno"> 1224</span>&#160;    &lt;&lt; m_computed(firstColm + i+2, firstColm+i+2) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01225"></a><span class="lineno"> 1225</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01226"></a><span class="lineno"> 1226</span>&#160;  <span class="keywordflow">if</span> (numext::is_exactly_zero(r))</div>
<div class="line"><a name="l01227"></a><span class="lineno"> 1227</span>&#160;  {</div>
<div class="line"><a name="l01228"></a><span class="lineno"> 1228</span>&#160;    m_computed(firstColm + i, firstColm + i) = m_computed(firstColm + j, firstColm + j);</div>
<div class="line"><a name="l01229"></a><span class="lineno"> 1229</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l01230"></a><span class="lineno"> 1230</span>&#160;  }</div>
<div class="line"><a name="l01231"></a><span class="lineno"> 1231</span>&#160;  c/=r;</div>
<div class="line"><a name="l01232"></a><span class="lineno"> 1232</span>&#160;  s/=r;</div>
<div class="line"><a name="l01233"></a><span class="lineno"> 1233</span>&#160;  m_computed(firstColm + i, firstColm) = r;</div>
<div class="line"><a name="l01234"></a><span class="lineno"> 1234</span>&#160;  m_computed(firstColm + j, firstColm + j) = m_computed(firstColm + i, firstColm + i);</div>
<div class="line"><a name="l01235"></a><span class="lineno"> 1235</span>&#160;  m_computed(firstColm + j, firstColm) = Literal(0);</div>
<div class="line"><a name="l01236"></a><span class="lineno"> 1236</span>&#160; </div>
<div class="line"><a name="l01237"></a><span class="lineno"> 1237</span>&#160;  JacobiRotation&lt;RealScalar&gt; J(c,-s);</div>
<div class="line"><a name="l01238"></a><span class="lineno"> 1238</span>&#160;  <span class="keywordflow">if</span> (m_compU)  m_naiveU.middleRows(firstColu, size+1).applyOnTheRight(firstColu + i, firstColu + j, J);</div>
<div class="line"><a name="l01239"></a><span class="lineno"> 1239</span>&#160;  <span class="keywordflow">else</span>          m_naiveU.applyOnTheRight(firstColu+i, firstColu+j, J);</div>
<div class="line"><a name="l01240"></a><span class="lineno"> 1240</span>&#160;  <span class="keywordflow">if</span> (m_compV)  m_naiveV.middleRows(firstRowW, size).applyOnTheRight(firstColW + i, firstColW + j, J);</div>
<div class="line"><a name="l01241"></a><span class="lineno"> 1241</span>&#160;}  <span class="comment">// end deflation 44</span></div>
<div class="line"><a name="l01242"></a><span class="lineno"> 1242</span>&#160; </div>
<div class="line"><a name="l01243"></a><span class="lineno"> 1243</span>&#160;<span class="comment">// acts on block from (firstCol+shift, firstCol+shift) to (lastCol+shift, lastCol+shift) [inclusive]</span></div>
<div class="line"><a name="l01244"></a><span class="lineno"> 1244</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l01245"></a><span class="lineno"> 1245</span>&#160;<span class="keywordtype">void</span> BDCSVD&lt;MatrixType, Options&gt;::deflation(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstCol, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> lastCol, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k,</div>
<div class="line"><a name="l01246"></a><span class="lineno"> 1246</span>&#160;                                            <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstRowW, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> firstColW, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> shift) {</div>
<div class="line"><a name="l01247"></a><span class="lineno"> 1247</span>&#160;  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l01248"></a><span class="lineno"> 1248</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l01249"></a><span class="lineno"> 1249</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> length = lastCol + 1 - firstCol;</div>
<div class="line"><a name="l01250"></a><span class="lineno"> 1250</span>&#160; </div>
<div class="line"><a name="l01251"></a><span class="lineno"> 1251</span>&#160;  Block&lt;MatrixXr,Dynamic,1&gt; col0(m_computed, firstCol+shift, firstCol+shift, length, 1);</div>
<div class="line"><a name="l01252"></a><span class="lineno"> 1252</span>&#160;  Diagonal&lt;MatrixXr&gt; fulldiag(m_computed);</div>
<div class="line"><a name="l01253"></a><span class="lineno"> 1253</span>&#160;  VectorBlock&lt;Diagonal&lt;MatrixXr&gt;,<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>&gt; diag(fulldiag, firstCol+shift, length);</div>
<div class="line"><a name="l01254"></a><span class="lineno"> 1254</span>&#160; </div>
<div class="line"><a name="l01255"></a><span class="lineno"> 1255</span>&#160;  <span class="keyword">const</span> RealScalar considerZero = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l01256"></a><span class="lineno"> 1256</span>&#160;  RealScalar maxDiag = diag.tail((std::max)(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>(1),length-1)).cwiseAbs().maxCoeff();</div>
<div class="line"><a name="l01257"></a><span class="lineno"> 1257</span>&#160;  RealScalar epsilon_strict = numext::maxi&lt;RealScalar&gt;(considerZero,NumTraits&lt;RealScalar&gt;::epsilon() * maxDiag);</div>
<div class="line"><a name="l01258"></a><span class="lineno"> 1258</span>&#160;  RealScalar epsilon_coarse = Literal(8) * NumTraits&lt;RealScalar&gt;::epsilon() * numext::maxi&lt;RealScalar&gt;(col0.cwiseAbs().maxCoeff(), maxDiag);</div>
<div class="line"><a name="l01259"></a><span class="lineno"> 1259</span>&#160; </div>
<div class="line"><a name="l01260"></a><span class="lineno"> 1260</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01261"></a><span class="lineno"> 1261</span>&#160;  assert(m_naiveU.allFinite());</div>
<div class="line"><a name="l01262"></a><span class="lineno"> 1262</span>&#160;  assert(m_naiveV.allFinite());</div>
<div class="line"><a name="l01263"></a><span class="lineno"> 1263</span>&#160;  assert(m_computed.allFinite());</div>
<div class="line"><a name="l01264"></a><span class="lineno"> 1264</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01265"></a><span class="lineno"> 1265</span>&#160; </div>
<div class="line"><a name="l01266"></a><span class="lineno"> 1266</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01267"></a><span class="lineno"> 1267</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;\ndeflate:&quot;</span> &lt;&lt; diag.head(k+1).transpose() &lt;&lt; <span class="stringliteral">&quot;  |  &quot;</span> &lt;&lt; diag.segment(k+1,length-k-1).transpose() &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01268"></a><span class="lineno"> 1268</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01269"></a><span class="lineno"> 1269</span>&#160; </div>
<div class="line"><a name="l01270"></a><span class="lineno"> 1270</span>&#160;  <span class="comment">//condition 4.1</span></div>
<div class="line"><a name="l01271"></a><span class="lineno"> 1271</span>&#160;  <span class="keywordflow">if</span> (diag(0) &lt; epsilon_coarse)</div>
<div class="line"><a name="l01272"></a><span class="lineno"> 1272</span>&#160;  {</div>
<div class="line"><a name="l01273"></a><span class="lineno"> 1273</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01274"></a><span class="lineno"> 1274</span>&#160;    std::cout &lt;&lt; <span class="stringliteral">&quot;deflation 4.1, because &quot;</span> &lt;&lt; diag(0) &lt;&lt; <span class="stringliteral">&quot; &lt; &quot;</span> &lt;&lt; epsilon_coarse &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01275"></a><span class="lineno"> 1275</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01276"></a><span class="lineno"> 1276</span>&#160;    diag(0) = epsilon_coarse;</div>
<div class="line"><a name="l01277"></a><span class="lineno"> 1277</span>&#160;  }</div>
<div class="line"><a name="l01278"></a><span class="lineno"> 1278</span>&#160; </div>
<div class="line"><a name="l01279"></a><span class="lineno"> 1279</span>&#160;  <span class="comment">//condition 4.2</span></div>
<div class="line"><a name="l01280"></a><span class="lineno"> 1280</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=1;i&lt;length;++i)</div>
<div class="line"><a name="l01281"></a><span class="lineno"> 1281</span>&#160;    <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(col0(i)) &lt; epsilon_strict)</div>
<div class="line"><a name="l01282"></a><span class="lineno"> 1282</span>&#160;    {</div>
<div class="line"><a name="l01283"></a><span class="lineno"> 1283</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01284"></a><span class="lineno"> 1284</span>&#160;      std::cout &lt;&lt; <span class="stringliteral">&quot;deflation 4.2, set z(&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;) to zero because &quot;</span> &lt;&lt; <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(col0(i)) &lt;&lt; <span class="stringliteral">&quot; &lt; &quot;</span> &lt;&lt; epsilon_strict &lt;&lt; <span class="stringliteral">&quot;  (diag(&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;)=&quot;</span> &lt;&lt; diag(i) &lt;&lt; <span class="stringliteral">&quot;)\n&quot;</span>;</div>
<div class="line"><a name="l01285"></a><span class="lineno"> 1285</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01286"></a><span class="lineno"> 1286</span>&#160;      col0(i) = Literal(0);</div>
<div class="line"><a name="l01287"></a><span class="lineno"> 1287</span>&#160;    }</div>
<div class="line"><a name="l01288"></a><span class="lineno"> 1288</span>&#160; </div>
<div class="line"><a name="l01289"></a><span class="lineno"> 1289</span>&#160;  <span class="comment">//condition 4.3</span></div>
<div class="line"><a name="l01290"></a><span class="lineno"> 1290</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=1;i&lt;length; i++)</div>
<div class="line"><a name="l01291"></a><span class="lineno"> 1291</span>&#160;    <span class="keywordflow">if</span> (diag(i) &lt; epsilon_coarse)</div>
<div class="line"><a name="l01292"></a><span class="lineno"> 1292</span>&#160;    {</div>
<div class="line"><a name="l01293"></a><span class="lineno"> 1293</span>&#160;<span class="preprocessor">#ifdef  EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01294"></a><span class="lineno"> 1294</span>&#160;      std::cout &lt;&lt; <span class="stringliteral">&quot;deflation 4.3, cancel z(&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;)=&quot;</span> &lt;&lt; col0(i) &lt;&lt; <span class="stringliteral">&quot; because diag(&quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot;)=&quot;</span> &lt;&lt; diag(i) &lt;&lt; <span class="stringliteral">&quot; &lt; &quot;</span> &lt;&lt; epsilon_coarse &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01295"></a><span class="lineno"> 1295</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01296"></a><span class="lineno"> 1296</span>&#160;      deflation43(firstCol, shift, i, length);</div>
<div class="line"><a name="l01297"></a><span class="lineno"> 1297</span>&#160;    }</div>
<div class="line"><a name="l01298"></a><span class="lineno"> 1298</span>&#160; </div>
<div class="line"><a name="l01299"></a><span class="lineno"> 1299</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01300"></a><span class="lineno"> 1300</span>&#160;  assert(m_naiveU.allFinite());</div>
<div class="line"><a name="l01301"></a><span class="lineno"> 1301</span>&#160;  assert(m_naiveV.allFinite());</div>
<div class="line"><a name="l01302"></a><span class="lineno"> 1302</span>&#160;  assert(m_computed.allFinite());</div>
<div class="line"><a name="l01303"></a><span class="lineno"> 1303</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01304"></a><span class="lineno"> 1304</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01305"></a><span class="lineno"> 1305</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;to be sorted: &quot;</span> &lt;&lt; diag.transpose() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l01306"></a><span class="lineno"> 1306</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;            : &quot;</span> &lt;&lt; col0.transpose() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l01307"></a><span class="lineno"> 1307</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01308"></a><span class="lineno"> 1308</span>&#160;  {</div>
<div class="line"><a name="l01309"></a><span class="lineno"> 1309</span>&#160;    <span class="comment">// Check for total deflation:</span></div>
<div class="line"><a name="l01310"></a><span class="lineno"> 1310</span>&#160;    <span class="comment">// If we have a total deflation, then we have to consider col0(0)==diag(0) as a singular value during sorting.</span></div>
<div class="line"><a name="l01311"></a><span class="lineno"> 1311</span>&#160;    <span class="keyword">const</span> <span class="keywordtype">bool</span> total_deflation = (col0.tail(length-1).array().abs()&lt;considerZero).<a class="code" href="group__Core__Module.html#ga4abe6022fbef6cda264ef2947a2be1a9">all</a>();</div>
<div class="line"><a name="l01312"></a><span class="lineno"> 1312</span>&#160; </div>
<div class="line"><a name="l01313"></a><span class="lineno"> 1313</span>&#160;    <span class="comment">// Sort the diagonal entries, since diag(1:k-1) and diag(k:length) are already sorted, let&#39;s do a sorted merge.</span></div>
<div class="line"><a name="l01314"></a><span class="lineno"> 1314</span>&#160;    <span class="comment">// First, compute the respective permutation.</span></div>
<div class="line"><a name="l01315"></a><span class="lineno"> 1315</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> *permutation = m_workspaceI.data();</div>
<div class="line"><a name="l01316"></a><span class="lineno"> 1316</span>&#160;    {</div>
<div class="line"><a name="l01317"></a><span class="lineno"> 1317</span>&#160;      permutation[0] = 0;</div>
<div class="line"><a name="l01318"></a><span class="lineno"> 1318</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p = 1;</div>
<div class="line"><a name="l01319"></a><span class="lineno"> 1319</span>&#160; </div>
<div class="line"><a name="l01320"></a><span class="lineno"> 1320</span>&#160;      <span class="comment">// Move deflated diagonal entries at the end.</span></div>
<div class="line"><a name="l01321"></a><span class="lineno"> 1321</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=1; i&lt;length; ++i)</div>
<div class="line"><a name="l01322"></a><span class="lineno"> 1322</span>&#160;        <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(diag(i))&lt;considerZero)</div>
<div class="line"><a name="l01323"></a><span class="lineno"> 1323</span>&#160;          permutation[p++] = i;</div>
<div class="line"><a name="l01324"></a><span class="lineno"> 1324</span>&#160; </div>
<div class="line"><a name="l01325"></a><span class="lineno"> 1325</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=1, j=k+1;</div>
<div class="line"><a name="l01326"></a><span class="lineno"> 1326</span>&#160;      <span class="keywordflow">for</span>( ; p &lt; length; ++p)</div>
<div class="line"><a name="l01327"></a><span class="lineno"> 1327</span>&#160;      {</div>
<div class="line"><a name="l01328"></a><span class="lineno"> 1328</span>&#160;             <span class="keywordflow">if</span> (i &gt; k)             permutation[p] = j++;</div>
<div class="line"><a name="l01329"></a><span class="lineno"> 1329</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (j &gt;= length)       permutation[p] = i++;</div>
<div class="line"><a name="l01330"></a><span class="lineno"> 1330</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (diag(i) &lt; diag(j)) permutation[p] = j++;</div>
<div class="line"><a name="l01331"></a><span class="lineno"> 1331</span>&#160;        <span class="keywordflow">else</span>                        permutation[p] = i++;</div>
<div class="line"><a name="l01332"></a><span class="lineno"> 1332</span>&#160;      }</div>
<div class="line"><a name="l01333"></a><span class="lineno"> 1333</span>&#160;    }</div>
<div class="line"><a name="l01334"></a><span class="lineno"> 1334</span>&#160; </div>
<div class="line"><a name="l01335"></a><span class="lineno"> 1335</span>&#160;    <span class="comment">// If we have a total deflation, then we have to insert diag(0) at the right place</span></div>
<div class="line"><a name="l01336"></a><span class="lineno"> 1336</span>&#160;    <span class="keywordflow">if</span>(total_deflation)</div>
<div class="line"><a name="l01337"></a><span class="lineno"> 1337</span>&#160;    {</div>
<div class="line"><a name="l01338"></a><span class="lineno"> 1338</span>&#160;      <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=1; i&lt;length; ++i)</div>
<div class="line"><a name="l01339"></a><span class="lineno"> 1339</span>&#160;      {</div>
<div class="line"><a name="l01340"></a><span class="lineno"> 1340</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> pi = permutation[i];</div>
<div class="line"><a name="l01341"></a><span class="lineno"> 1341</span>&#160;        <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(diag(pi))&lt;considerZero || diag(0)&lt;diag(pi))</div>
<div class="line"><a name="l01342"></a><span class="lineno"> 1342</span>&#160;          permutation[i-1] = permutation[i];</div>
<div class="line"><a name="l01343"></a><span class="lineno"> 1343</span>&#160;        <span class="keywordflow">else</span></div>
<div class="line"><a name="l01344"></a><span class="lineno"> 1344</span>&#160;        {</div>
<div class="line"><a name="l01345"></a><span class="lineno"> 1345</span>&#160;          permutation[i-1] = 0;</div>
<div class="line"><a name="l01346"></a><span class="lineno"> 1346</span>&#160;          <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l01347"></a><span class="lineno"> 1347</span>&#160;        }</div>
<div class="line"><a name="l01348"></a><span class="lineno"> 1348</span>&#160;      }</div>
<div class="line"><a name="l01349"></a><span class="lineno"> 1349</span>&#160;    }</div>
<div class="line"><a name="l01350"></a><span class="lineno"> 1350</span>&#160; </div>
<div class="line"><a name="l01351"></a><span class="lineno"> 1351</span>&#160;    <span class="comment">// Current index of each col, and current column of each index</span></div>
<div class="line"><a name="l01352"></a><span class="lineno"> 1352</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> *realInd = m_workspaceI.data()+length;</div>
<div class="line"><a name="l01353"></a><span class="lineno"> 1353</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> *realCol = m_workspaceI.data()+2*length;</div>
<div class="line"><a name="l01354"></a><span class="lineno"> 1354</span>&#160; </div>
<div class="line"><a name="l01355"></a><span class="lineno"> 1355</span>&#160;    <span class="keywordflow">for</span>(<span class="keywordtype">int</span> pos = 0; pos&lt; length; pos++)</div>
<div class="line"><a name="l01356"></a><span class="lineno"> 1356</span>&#160;    {</div>
<div class="line"><a name="l01357"></a><span class="lineno"> 1357</span>&#160;      realCol[pos] = pos;</div>
<div class="line"><a name="l01358"></a><span class="lineno"> 1358</span>&#160;      realInd[pos] = pos;</div>
<div class="line"><a name="l01359"></a><span class="lineno"> 1359</span>&#160;    }</div>
<div class="line"><a name="l01360"></a><span class="lineno"> 1360</span>&#160; </div>
<div class="line"><a name="l01361"></a><span class="lineno"> 1361</span>&#160;    <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = total_deflation?0:1; i &lt; length; i++)</div>
<div class="line"><a name="l01362"></a><span class="lineno"> 1362</span>&#160;    {</div>
<div class="line"><a name="l01363"></a><span class="lineno"> 1363</span>&#160;      <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> pi = permutation[length - (total_deflation ? i+1 : i)];</div>
<div class="line"><a name="l01364"></a><span class="lineno"> 1364</span>&#160;      <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> J = realCol[pi];</div>
<div class="line"><a name="l01365"></a><span class="lineno"> 1365</span>&#160; </div>
<div class="line"><a name="l01366"></a><span class="lineno"> 1366</span>&#160;      <span class="keyword">using</span> std::swap;</div>
<div class="line"><a name="l01367"></a><span class="lineno"> 1367</span>&#160;      <span class="comment">// swap diagonal and first column entries:</span></div>
<div class="line"><a name="l01368"></a><span class="lineno"> 1368</span>&#160;      swap(diag(i), diag(J));</div>
<div class="line"><a name="l01369"></a><span class="lineno"> 1369</span>&#160;      <span class="keywordflow">if</span>(i!=0 &amp;&amp; J!=0) swap(col0(i), col0(J));</div>
<div class="line"><a name="l01370"></a><span class="lineno"> 1370</span>&#160; </div>
<div class="line"><a name="l01371"></a><span class="lineno"> 1371</span>&#160;      <span class="comment">// change columns</span></div>
<div class="line"><a name="l01372"></a><span class="lineno"> 1372</span>&#160;      <span class="keywordflow">if</span> (m_compU) m_naiveU.col(firstCol+i).segment(firstCol, length + 1).swap(m_naiveU.col(firstCol+J).segment(firstCol, length + 1));</div>
<div class="line"><a name="l01373"></a><span class="lineno"> 1373</span>&#160;      <span class="keywordflow">else</span>         m_naiveU.col(firstCol+i).segment(0, 2)                .swap(m_naiveU.col(firstCol+J).segment(0, 2));</div>
<div class="line"><a name="l01374"></a><span class="lineno"> 1374</span>&#160;      <span class="keywordflow">if</span> (m_compV) m_naiveV.col(firstColW + i).segment(firstRowW, length).swap(m_naiveV.col(firstColW + J).segment(firstRowW, length));</div>
<div class="line"><a name="l01375"></a><span class="lineno"> 1375</span>&#160; </div>
<div class="line"><a name="l01376"></a><span class="lineno"> 1376</span>&#160;      <span class="comment">//update real pos</span></div>
<div class="line"><a name="l01377"></a><span class="lineno"> 1377</span>&#160;      <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> realI = realInd[i];</div>
<div class="line"><a name="l01378"></a><span class="lineno"> 1378</span>&#160;      realCol[realI] = J;</div>
<div class="line"><a name="l01379"></a><span class="lineno"> 1379</span>&#160;      realCol[pi] = i;</div>
<div class="line"><a name="l01380"></a><span class="lineno"> 1380</span>&#160;      realInd[J] = realI;</div>
<div class="line"><a name="l01381"></a><span class="lineno"> 1381</span>&#160;      realInd[i] = pi;</div>
<div class="line"><a name="l01382"></a><span class="lineno"> 1382</span>&#160;    }</div>
<div class="line"><a name="l01383"></a><span class="lineno"> 1383</span>&#160;  }</div>
<div class="line"><a name="l01384"></a><span class="lineno"> 1384</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01385"></a><span class="lineno"> 1385</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;sorted: &quot;</span> &lt;&lt; diag.transpose().format(bdcsvdfmt) &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01386"></a><span class="lineno"> 1386</span>&#160;  std::cout &lt;&lt; <span class="stringliteral">&quot;      : &quot;</span> &lt;&lt; col0.transpose() &lt;&lt; <span class="stringliteral">&quot;\n\n&quot;</span>;</div>
<div class="line"><a name="l01387"></a><span class="lineno"> 1387</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01388"></a><span class="lineno"> 1388</span>&#160; </div>
<div class="line"><a name="l01389"></a><span class="lineno"> 1389</span>&#160;  <span class="comment">//condition 4.4</span></div>
<div class="line"><a name="l01390"></a><span class="lineno"> 1390</span>&#160;  {</div>
<div class="line"><a name="l01391"></a><span class="lineno"> 1391</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = length-1;</div>
<div class="line"><a name="l01392"></a><span class="lineno"> 1392</span>&#160;    <span class="keywordflow">while</span>(i&gt;0 &amp;&amp; (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(diag(i))&lt;considerZero || <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(col0(i))&lt;considerZero)) --i;</div>
<div class="line"><a name="l01393"></a><span class="lineno"> 1393</span>&#160;    <span class="keywordflow">for</span>(; i&gt;1;--i)</div>
<div class="line"><a name="l01394"></a><span class="lineno"> 1394</span>&#160;       <span class="keywordflow">if</span>( (diag(i) - diag(i-1)) &lt; NumTraits&lt;RealScalar&gt;::epsilon()*maxDiag )</div>
<div class="line"><a name="l01395"></a><span class="lineno"> 1395</span>&#160;      {</div>
<div class="line"><a name="l01396"></a><span class="lineno"> 1396</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_DEBUG_VERBOSE</span></div>
<div class="line"><a name="l01397"></a><span class="lineno"> 1397</span>&#160;        std::cout &lt;&lt; <span class="stringliteral">&quot;deflation 4.4 with i = &quot;</span> &lt;&lt; i &lt;&lt; <span class="stringliteral">&quot; because &quot;</span> &lt;&lt; diag(i) &lt;&lt; <span class="stringliteral">&quot; - &quot;</span> &lt;&lt; diag(i-1) &lt;&lt; <span class="stringliteral">&quot; == &quot;</span> &lt;&lt; (diag(i) - diag(i-1)) &lt;&lt; <span class="stringliteral">&quot; &lt; &quot;</span> &lt;&lt; NumTraits&lt;RealScalar&gt;::epsilon()*<span class="comment">/*diag(i)*/</span>maxDiag &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l01398"></a><span class="lineno"> 1398</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01399"></a><span class="lineno"> 1399</span>&#160;        eigen_internal_assert(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(diag(i) - diag(i-1))&lt;epsilon_coarse &amp;&amp; <span class="stringliteral">&quot; diagonal entries are not properly sorted&quot;</span>);</div>
<div class="line"><a name="l01400"></a><span class="lineno"> 1400</span>&#160;        deflation44(firstCol, firstCol + shift, firstRowW, firstColW, i-1, i, length);</div>
<div class="line"><a name="l01401"></a><span class="lineno"> 1401</span>&#160;      }</div>
<div class="line"><a name="l01402"></a><span class="lineno"> 1402</span>&#160;  }</div>
<div class="line"><a name="l01403"></a><span class="lineno"> 1403</span>&#160; </div>
<div class="line"><a name="l01404"></a><span class="lineno"> 1404</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01405"></a><span class="lineno"> 1405</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j=2;j&lt;length;++j)</div>
<div class="line"><a name="l01406"></a><span class="lineno"> 1406</span>&#160;    assert(diag(j-1)&lt;=diag(j) || <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(diag(j))&lt;considerZero);</div>
<div class="line"><a name="l01407"></a><span class="lineno"> 1407</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01408"></a><span class="lineno"> 1408</span>&#160; </div>
<div class="line"><a name="l01409"></a><span class="lineno"> 1409</span>&#160;<span class="preprocessor">#ifdef EIGEN_BDCSVD_SANITY_CHECKS</span></div>
<div class="line"><a name="l01410"></a><span class="lineno"> 1410</span>&#160;  assert(m_naiveU.allFinite());</div>
<div class="line"><a name="l01411"></a><span class="lineno"> 1411</span>&#160;  assert(m_naiveV.allFinite());</div>
<div class="line"><a name="l01412"></a><span class="lineno"> 1412</span>&#160;  assert(m_computed.allFinite());</div>
<div class="line"><a name="l01413"></a><span class="lineno"> 1413</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l01414"></a><span class="lineno"> 1414</span>&#160;}  <span class="comment">// end deflation</span></div>
<div class="line"><a name="l01415"></a><span class="lineno"> 1415</span>&#160; </div>
<div class="line"><a name="l01422"></a><span class="lineno"> 1422</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l01423"></a><span class="lineno"> 1423</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l01424"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a7eaba4620ea3dcbd044fcbe0a874ae6d"> 1424</a></span>&#160;<a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>, Options&gt; <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;::bdcSvd</a>()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l01425"></a><span class="lineno"> 1425</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD&lt;PlainObject, Options&gt;</a>(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l01426"></a><span class="lineno"> 1426</span>&#160;}</div>
<div class="line"><a name="l01427"></a><span class="lineno"> 1427</span>&#160; </div>
<div class="line"><a name="l01434"></a><span class="lineno"> 1434</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l01435"></a><span class="lineno"> 1435</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Options&gt;</div>
<div class="line"><a name="l01436"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a7c12a99afc2f6982d162e7e59236f946"> 1436</a></span>&#160;<a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>, Options&gt; <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;::bdcSvd</a>(</div>
<div class="line"><a name="l01437"></a><span class="lineno"> 1437</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> computationOptions)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l01438"></a><span class="lineno"> 1438</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1BDCSVD.html">BDCSVD&lt;PlainObject, Options&gt;</a>(*<span class="keyword">this</span>, computationOptions);</div>
<div class="line"><a name="l01439"></a><span class="lineno"> 1439</span>&#160;}</div>
<div class="line"><a name="l01440"></a><span class="lineno"> 1440</span>&#160; </div>
<div class="line"><a name="l01441"></a><span class="lineno"> 1441</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l01442"></a><span class="lineno"> 1442</span>&#160; </div>
<div class="line"><a name="l01443"></a><span class="lineno"> 1443</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="aclassEigen_1_1Array_html"><div class="ttname"><a href="classEigen_1_1Array.html">Eigen::Array&lt; RealScalar, Dynamic, 1 &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html"><div class="ttname"><a href="classEigen_1_1BDCSVD.html">Eigen::BDCSVD</a></div><div class="ttdoc">class Bidiagonal Divide and Conquer SVD</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:97</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_a1d4028e15977308117e7ead7a21feee9"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a1d4028e15977308117e7ead7a21feee9">Eigen::BDCSVD::compute</a></div><div class="ttdeci">BDCSVD &amp; compute(const MatrixType &amp;matrix)</div><div class="ttdoc">Method performing the decomposition of given matrix. Computes Thin/Full unitaries U/V if specified us...</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:206</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_a2d768a9877f5f69f49432d447b552bfe"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a2d768a9877f5f69f49432d447b552bfe">Eigen::BDCSVD::cols</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_a30778887eb456715a333ccf9cb75f14e"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a30778887eb456715a333ccf9cb75f14e">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">EIGEN_DEPRECATED BDCSVD(const MatrixType &amp;matrix, unsigned int computationOptions)</div><div class="ttdoc">Constructor performing the decomposition of given matrix using specified options for computing unitar...</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:194</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_a586d8a4d76bb40f315f8ae290419abf3"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a586d8a4d76bb40f315f8ae290419abf3">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">BDCSVD(const MatrixType &amp;matrix)</div><div class="ttdoc">Constructor performing the decomposition of given matrix, using the custom options specified with the...</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:177</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_a7d9fac78e0c239b2e8e92cd189932f21"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a7d9fac78e0c239b2e8e92cd189932f21">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">EIGEN_DEPRECATED BDCSVD(Index rows, Index cols, unsigned int computationOptions)</div><div class="ttdoc">Default Constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:167</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_a9c247985636005f4aef20bc92f713cd3"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#a9c247985636005f4aef20bc92f713cd3">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">BDCSVD()</div><div class="ttdoc">Default Constructor.</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:139</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::BDCSVD::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_ada8a7edd2ddc8ab10fdea4b1b7c1b838"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#ada8a7edd2ddc8ab10fdea4b1b7c1b838">Eigen::BDCSVD::compute</a></div><div class="ttdeci">EIGEN_DEPRECATED BDCSVD &amp; compute(const MatrixType &amp;matrix, unsigned int computationOptions)</div><div class="ttdoc">Method performing the decomposition of given matrix, as specified by the computationOptions parameter...</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:218</div></div>
<div class="ttc" id="aclassEigen_1_1BDCSVD_html_afa37310e3f27088f3e825f59ab822ef9"><div class="ttname"><a href="classEigen_1_1BDCSVD.html#afa37310e3f27088f3e825f59ab822ef9">Eigen::BDCSVD::BDCSVD</a></div><div class="ttdeci">BDCSVD(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> BDCSVD.h:148</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a98bb9a0f705c6dfde85b0bfff31bf88f"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a98bb9a0f705c6dfde85b0bfff31bf88f">Eigen::MatrixBase::Identity</a></div><div class="ttdeci">static const IdentityReturnType Identity()</div><div class="ttdef"><b>Definition:</b> CwiseNullaryOp.h:801</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition:</b> Matrix.h:182</div></div>
<div class="ttc" id="aclassEigen_1_1Ref_html"><div class="ttname"><a href="classEigen_1_1Ref.html">Eigen::Ref</a></div><div class="ttdoc">A matrix or vector expression mapping an existing expression.</div><div class="ttdef"><b>Definition:</b> Ref.h:285</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html"><div class="ttname"><a href="classEigen_1_1SVDBase.html">Eigen::SVDBase</a></div><div class="ttdoc">Base class of SVD algorithms.</div><div class="ttdef"><b>Definition:</b> SVDBase.h:120</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a5f12efcb791eb007d4a4890ac5255ac4"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">Eigen::SVDBase::computeV</a></div><div class="ttdeci">bool computeV() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:284</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a6229a37997eca1072b52cca5ee7a2bec"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a6229a37997eca1072b52cca5ee7a2bec">Eigen::SVDBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdef"><b>Definition:</b> SVDBase.h:130</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a705a7c2709e1624ccc19aa748a78d473"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">Eigen::SVDBase::computeU</a></div><div class="ttdeci">bool computeU() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:282</div></div>
<div class="ttc" id="agroup__Core__Module_html_ga4abe6022fbef6cda264ef2947a2be1a9"><div class="ttname"><a href="group__Core__Module.html#ga4abe6022fbef6cda264ef2947a2be1a9">Eigen::placeholders::all</a></div><div class="ttdeci">static const Eigen::internal::all_t all</div><div class="ttdef"><b>Definition:</b> IndexedViewHelper.h:189</div></div>
<div class="ttc" id="agroup__enums_html_gga45fe06e29902b7a2773de05ba27b47a1ae12d0f8f869c40c76128260af2242bc8"><div class="ttname"><a href="group__enums.html#gga45fe06e29902b7a2773de05ba27b47a1ae12d0f8f869c40c76128260af2242bc8">Eigen::Aligned</a></div><div class="ttdeci">@ Aligned</div><div class="ttdef"><b>Definition:</b> Constants.h:242</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea580b2a3cafe585691e789f768fb729bf">Eigen::InvalidInput</a></div><div class="ttdeci">@ InvalidInput</div><div class="ttdef"><b>Definition:</b> Constants.h:451</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">Eigen::NoConvergence</a></div><div class="ttdeci">@ NoConvergence</div><div class="ttdef"><b>Definition:</b> Constants.h:448</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga8a779d79defc9f822fa6ff5869c2ba6b"><div class="ttname"><a href="group__matrixtypedefs.html#ga8a779d79defc9f822fa6ff5869c2ba6b">Eigen::MatrixX</a></div><div class="ttdeci">Matrix&lt; Type, Dynamic, Dynamic &gt; MatrixX</div><div class="ttdoc">[c++11] Dynamic×Dynamic matrix of type Type.</div><div class="ttdef"><b>Definition:</b> Matrix.h:536</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_af4f536e8ea56702e63088efb3706d1f0"><div class="ttname"><a href="namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">Eigen::sqrt</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sqrt_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sqrt(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a554f30542cc2316add4b1ea0a492ff02"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Eigen::EigenBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdoc">The interface type of indices.</div><div class="ttdef"><b>Definition:</b> EigenBase.h:41</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_ae106171b6fefd3f7af108a8283de36c9"><div class="ttname"><a href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">Eigen::EigenBase::size</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:69</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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